The [log] where you can find from calculator is the common Example 3: with a coefficient in front of base. Nov 17, 2016 · Indices can be integral or fractional, positive or negative. This Sep 2, 2021 · Example 1: Simplify. 6 4a ÷ 6 a. Simplify the following (i) 6 4a ÷ 6 a (ii) 4 3 ÷ 4 (iii) 5 3 – 5 2. 3m 11s. You are given a short test at the end. Given below is the representation of the index of a number. Example 3: Two Way Lookup. The relationship between P p and P pk is similar to that between C p and C pk. GCSE Maths made easy Algeba covering Foundation and Higher level. Fraction Indices 7. y = n ax , x ∈. The ML Aggarwal Solutions Class 11 Maths has been made to be user-friendly in an effort to lessen student stress and give the ML Aggarwal Solutions a clean appearance. Nov 24, 2022 · Triclinic. Quotient Law: a m / a n =a m−n. 2-y. 32. We can rewrite the radical in its rational exponent form, then reduce each exponent fraction. Jan 22, 2020 · Solution of Ch-Test Questions on Indices of ML Aggarwal for ICSE Class 9 Mathematics Ch-8. The number 3 is called the power or index. • Negative index rule: a − n = 1 a n. NCERT Solutions for Class 12 Chemistry are drafted by the faculty at BYJU’S to help students learn all the complex concepts efficiently. The above example will give us, ( from this value, 4 will cut the fourth root) Or we can solve the above simply making have the same power with the given root (which in this case is 4). 1 22. 9 = 104+6x 9 = 10 4 + 6 x Solution. Checking if a function is increasing or decreasing in whole domain. 5z = 2160, find the value of x, y, z. Worked solution to the above core 1 question on indices and differentiation. Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths learn how to simplify negative indices and fractional indices. find roots using indices. 1) Ge has the same crystal structure (diamond) as Si, with a lattice constant of a = 5. = INDEX (E1:E10, MATCH (. This is a very basic intro to ensure fraction work is fully fluent and moves on with some algebraic fractions. ML Aggarwal Solutions for Class 9 Maths Chapter 8 Indices is designed by individual subject experts at BYJU’S, to help students solve the exercise problems of the chapter. a1 – x direction, a2 – y direction, and a3 – z direction. Consider: a 2 × a 3 = (a × a) × (a × a × a) = a 2 + 3. The notes and questions for Surds & Indices - Introduction and Examples (with Solutions) have been prepared according to the Banking Exams exam syllabus. Question 2: Indices Question 1 with Fully Worked Answer. University of New South Wales. For instance, in the expression 3 5, 5 is the index, indicating that 3 is multiplied by itself five times. Zakariyah. Write 1/27 in the index forms. The page below will explain why. along the given three directions. If then . It explains the causes of phenomena like sunrise, sunset, and changing of the seasons. A typical response is 4 = 2 2. Aug 21, 2023 · Worked Examples. Exponents are also called Powers or Indices. Write each of the following expanded forms in index form: Solution: Example 3 We learned Derivatives in the last chapter, in Chapter 5 Class 12. If m is a positive integer, then axaxaxa—- upto m terms, is written as a m ; where ‘a’ is called the base and m is called the power (or exponent or index). The base is 3, so rearrange both sides as powers of 3. It is a solution formed by gases, among which nitrogen and oxygen stand out, which are present in the atmosphere. Here, you have to apply the basic division law. We have, Form 2 Questions and Answers on Indices and logarithms. Try the free Mathway calculator and problem solver below to practice various math topics. Indices show repeated multiplication, eg. a = 7 , n = 2. The index represents the number of times a number has to be multiplied by itself. Here are the solutions: Figure 22. If another significant cash outflow occurs elsewhere in the company at date 1, the project 3 may have to be rejected. Example: Input: arr = [1, 1, 4, 17]Output: 2Explanation: The element 1 at index 0, is a power of 0The element Laws of Exponents. To solve this, you must recall: X 1 = X (any number raised to the power of one is that same number) Therefore 4 = 4 1. These solutions for Indices And Cube Root are extremely popular among class 8 students for Math Indices And Cube Root Solutions come handy for quickly completing your homework and preparing for exams. this purpose. 71−x = 43x+1 7 1 − x = 4 3 x + 1 Solution. Get NCERT solutions for Class 12 Maths free with videos. Mar 20, 2021 · Solutions of the second chapter has been provided in detail. So, suppose we have We write this as ‘4 to the power 3’: 4 4 4 × × 43. Laws of indices, examples and solutions. or absolute or invariant or direct or vector notation. PI Formula = 1 + NPV / Initial Investment Required. 9 x + 3 2 x − 1 = 53. Suppose, we have a value √3 3. Geometric Progression; Binomial Theorem & Pascal's Triangle The following diagram shows how to divide exponents by subtracting indices. If (p + q)-1 (p-1 + q-1) = paqb, prove that a + b + 2 = 0, where p and q are different positive primes. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. x m × x n = x m+n Feb 22, 2022 · The Miller Indices are also enclosed within standard brackets (…. Now, we need to add the arguments of the MATCH function. e. Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths to help students learn the multiplication rule, division rule and power rule of indices. 1. Solving equations where the power is to be found by expressing each term in the same base. For example, for 3 2, 2 is the index and 3 is the base. Miller Indices: (100) So the surface/plane illustrated is the (100) plane of the cubic crystal. Any number with an exponent of 0 is 1. Geometric Progression; Binomial Theorem & Pascal's Triangle Indices - The basics (Laws) Indices - Examples. In this Chapter we will learn the applications of those derivatives. 3. Miller Indices are a 3-dimensional coordinate system for crystals, based on the unit cell. So. e7+2x−3 =0 e 7 + 2 x − 3 = 0 Solution. the bases of these two numbers are equal. This is the first law of Apr 9, 2024 · The profitability index would not work if funds are also insufficient beyond the period of initial investment. = 1/a1, l = 1/a2, and m = 1/a3. Rule 1: = √rxs = √r x √s. In this course, we are going to learn through worked out examples. How we work with fractional indices. For example, the formula =INDEX(A1:D6, 4, 3) returns the value at the intersection of the 4 th row and 3 rd column in range A1:D6, which is the value in cell C4. Indices. • Zero index rule: a 0 = 1. Mathematics Solutions Solutions for Class 8 Math Chapter 3 Indices And Cube Root are provided here with simple step-by-step explanations. Example : If d³ = 5³ then as powers are equal , d = 5. MATCH Function: Finds the Position baed on a Lookup Value. Statistics. Some common examples of Miller Indices on a cube include [111], the body diagonal; [110], the face diagonal; and (100), the face plane. Nov 26, 2020 · Learning Objectives. e4−7x+11 = 20 e 4 − 7 x + 11 = 20 Solution. The first argument is the reference against which it will find the lookup value. The word "index" means "power". Some of them are broad based indices, which attempt to replicate a market, and some are more specialised ones, which attempt to capture an individual segment of the market. . Example 1: Selina Concise Mathematics - Part I Solutions for Class 9 Maths ICSE Chapter 7: Get free access to Indices (Exponents) Class 9 Solutions which includes all the exercises with solved solutions. Combine it with the MATCH function. 564 nm. Here, 4 is the greatest perfect square factor of 20. Once index notation is introduced the index laws arise naturally when simplifying numerical and algebraic expressions. PI = 1 + 0. Definitions. In this example: 82 = 8 × 8 = 64. Show step. You may assume that each input would have exactly one solution, and you may not use the same element twice. Example: (2 3) 4 = 2 12 . Similar to the DJIA, the Nikkei 225 is calculated by adding up the prices of all 225 stocks and dividing the total by a divisor. 1: Though both Lakes A and B have the same amount of birds and the same number of different species, their diversity is different. Sequences & Series. Get access to thousands of educational resources. 63 / 5000. Laws of indices Simplify 1) (5p 2 × 4p 3 × 5p 5) 3 2) MATH2901 2018 Midsession Exam with solutions. How to simplify negative powers? Indices - Fractional Powers. Show Video Lesson. ) when one is specifying a unique surface such as that being considered here. Note 0 0 is meaningless. Lessons ( 99 ) SHARE. 10 8 instead of Selina Solutions for Class 9 Maths Chapter 7- Indices [Exponents] The Chapter 7 of class 9 takes the students to a new topic Indices[exponents]. Join this channel to get access to perks:→ htt Process Capability Index shows how closely a process is able to produce the output to its overall specifications. 6 4a ÷ 6 a = 6 4a – a = 6 3a. Selina solutions for Mathematics Concise Mathematics Class 9 ICSE CISCE 7 (Indices (Exponents)) include all questions with answers and detailed explanations. A-Level Maths Edexcel C1 June 2009 Q9b. 4) where a 1, a 2 and a. Rewrite 8√x6y2 as a reduced radical with root 4. Indices - ExamSolutions %. The task is to return the maximum frequency of X. Question 1: If 2x. Show Step-by-step Solutions. Example 1: Determine if $$5^4\times 5^3$$ has a positive, negative or zero index. When multiplying numbers in exponent notation with the same base, we can add the exponents. The following diagrams show the rules of indices or laws of indices. Example: 2 3 ×2 4 = 2 3+4 = 2 7 =128. The (110) surface Question 15 (***) The points ( 2,14 ) and ( 6,126 ) lie on the curve with equation. Reduce the result to the smallest integer. For example, the solution to (c) are and , i. The calculation is done by separating the formula into two halves. Miller Indices - Illinois Institute of Technology Given an array of integers nums and an integer target, return indices of the two numbers such that they add up to target. Maths : Indices : Multiplication Rule In this tutorial you are shown the multiplication rule for indices. Example 2: Lookup to the Left. Let’s Combine Them to Create a Powerhouse (INDEX + MATCH) Example 1: A simple Lookup Using INDEX MATCH Combo. Introduction To Exponents (Indices) Examples of positive exponents and zero exponent. This and others are 26) Without using a calculator simplify (√ ) freely available online. This tutorial will show you how this is done Indices Question 4 with Fully Worked Answer. If column_num is omitted, row_num is required. Links to other subjects. The plural of "index" is "indices". Here you will find video tutorials on powers and indices. 3y. Examples, solutions and videos to help GCSE Maths students learn about the multiplication and division rules of indices. HOW TO FIND MILLER INDICES. Indices or Powers. Here we need to note, If the powers are odd numbers then the bases will Examples of solutions in everyday life. 64 Angstroms = 0. Basically, they are a shorthand way of writing multiplications of the same number. Take the reciprocals of the intercepts. 3 days ago · The index of a number can also be zero or negative. The CPI might overstate changes in the cost of living because it doesn't always account for how people SOLUTIONS: ECE 305 Homework 1: Week 1. Solution. 2 22. 1 day ago · Given an array arr[] with N non-negative integers, find the maximum number of elements that are the same non-negative powers of their indices. Thus, if the index of any number is negative, then the value The Consumer Price Index (CPI) The country of Ambrosia calculates inflation using a consumer price index (CPI). Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths. An index in the form of a fraction can be represented as the radical Jul 31, 2023 · What does Index mean in Mathematics? In the realm of mathematics, an index is a figure that signifies the number of times a particular number is multiplied by itself. pdf. Click on a Chapter below to begin. The reciprocals of 1 and ∞ are 1 and 0 respectively, thus yielding. (Consider d,h, n denote numbers ) 1 ) If there are two numbers with exponential values and these two powers are equal then both. Leaving Certificate Points. Simplify and leave your answer in index form. Use the denominator to find the root of the number or letter. We use the index form usually with 10 as the base for every large numbers or very small numbers e. The exponent of a number says how many times to use the number in a multiplication. 2. For example, is it much easier to write 3 5 than 3 × 3 × 3 × 3 × 3. Nov 16, 2022 · 23x = 10 2 3 x = 10 Solution. Example. This section covers Indices and the uses of Indices in algebra. Indices Examples | Questions on Laws of Indices. It decides how consistent we are to our average performance. Apr 6, 2020 · Another example of a price-weighted index is the Nikkei 225 in Japan. Solve for x in: 9x + 32x - 1 = 53. Calculating Consumer Price Indices in Practice. You are viewing an excerpt of this Topic. where a and n are non zero constants. Quick Tips and Tricks. Worked Examples 7. If we calculated the profitability index using the NPV / I approach, then you take the £10,000 NPV for A and divide it by the initial investment in A Simplifying expressions using the laws of indices Simplifying indices Indices show where a number has been multiplied by itself, eg squared or cubed, or to show roots of numbers, eg square root. Indices Fractional Indices: Law of Indices: How to simplify algebraic expressions. Understanding Match Type Argument in MATCH Function. Smoke (solid in gas). Solutions are mixtures that are present in several areas, both in nature and in the home and in industries. So, a 0 = 1, for a ≠ 0. 8. Example 1: Find the numerical value for each of the following (not containing exponents): (i) 8 0 (ii)5-10 (iii)27 2/3. PI = 1 + 1277. Between 2016 and 2017 the CPI increased from 200 to 220 . (b) 24 × (1 8) − 1 × 40. Leaving Cert Exam solutions; Fermat's Last Theorem. Introduction. It involves using the rules of indices. We know that, √20 = 2*2*5. Example 2: Simplify. 4 4 4 = 43. Dec 18, 2023 · Here are the main laws of indices with examples: Product Law: a m × a n = a m+n. Six Rules of Surds. Other Examples. √20 = 22 ∗ 5. If , find x and y, where a, b are different positive primes. When dividing numbers in exponent notation with the same base, we subtract the exponents. 26. This video shows a guide to indices and powers. 1. In words: 8 2 could be called "8 to the second power", "8 to the power 2" or simply "8 squared". Next, ask the class if there is a way to write 2 and 4 with the same base. This index includes 225 stocks listed on the Tokyo Stock Exchange and is considered a benchmark for the Japanese stock market. Checking if a function is increasing or decreasing in an interval. 1: Evaluate the following: (a) 5x − 2y × 2x − 5y2. Let us solve some examples here: Example 1: NCERT Class 9 Science Chapter 8 explains the concept of motion, and types of motion with relevant examples for a clear understanding of the concept. From the above, Hence, for roots, we divide the indices, while for powers we multiply the indices. Indices - Simplifying Negative Powers. Surds and Indices. Members can access additional questions on this topic, including exam style Indices - ExamSolutions %. The methods used in different countries are not exactly the same, but they have much in common. The index P p represents the allowable tolerance spread relative to the actual spread of the data when the data follow a normal distribution. arr[i] = iX, where X is a non negative number. 2: The three blue columns show the steps to calculate D for Lake A, while the three gray columns show the steps to calculate D for Lake B. These numbers are governed by several indices rules that we will discuss here. For further discussion of Miller indices with examples, watch the videos linked here: Video 11-5: Miller indices example (2 minutes) Video 11-6: Miller indices of 0 (5 minutes) This video teaches you How to solve Indices and properties of indices. View Solution. For example, if , then , where index 4 becomes the logarithms and 2 as the base. The unit vectors are called base vectors when used for. Enter the formula as: = INDEX (. This will clear students' doubts about questions and improve their application Nov 14, 2021 · Example 10. 1/27 = 1/3 x 1/3 x 1/3 = (1/3) 3 this is an index form for the number 1/27 which can also be written as 27-1. The index only applies to the variable b and not the coefficient 3. Hence compute the value of 3x. For example: in 5 3, 5 is the "base" and 3 is the "index". Very basic rules of indices in this video. The process capability index of P p and P pk are sometimes referred to as long-term capability or performance indices. 5 3 = 5 \(\times\) 5 \(\times\) 5. 2) (x m) n = x mn. Notice how the index only affects the variable b. From the above computation, we can come to the conclusion that ABC Company should invest in the project as PI is more than 1. Laws of Indices and Indices problems examples. A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. need to multiply both indices together and raise it to the same base (a m) n = a mn. TeeJay Maths Book . Put the term over 1. 1) x m × x n = a m+n. Here is a set of practice problems to accompany the Solving Exponential Equations section of the Exponential and Logarithm Functions chapter Indices GCSE Maths revision worked exam questions (include fractional and negative powers) Solving equations in which the power is to be found. Consider: This is the second law of exponents: Simplify the following expressions, giving your answers Apr 15, 2024 · By using the NPV method, we would now calculate profitability index (PI) –. In general, , we call them as common logarithms (base 10). Find the atomic density (atoms/cm3) and the spacing between nearest-‐neighbor atoms in Ge. For example: `2^3 xx 2^4` `= (2xx2xx2) xx (2xx2xx2xx2) = 2^7` which is the same as adding the indices. 1 The purpose of this chapter is to provide a general description of the ways in which consumer price indices (CPIs) are calculated in practice. The Consumer Price Index (CPI) is a measure of the average change in prices of a typical basket of goods and services over time. It helps students understand uniform and non-uniform motion. After studying this section, you will be able to: divide and multiply algebraic expressions using indices. \[a^{n}\] = \[a \ast a \ast a \ast a\cdot \cdot \cdot \cdot\] (n times) Here, Because of the redundancy, and to be consistent with other crystal systems, many crystallographers today use only three indices for hexagonal minerals. Evaluate the following indicial expressions, giving the final answers as exact simplified fractions. g. All of the other index laws are based on the simple facts above. For further details on complex numbers, kindly refer to ‘Complex Numbers Explained with Worked Examples’ by Shefiu S. Try it yourself: Jun 1, 2022 · To solve the equation, we need to remember that the equal sign means the two sides of the equation are equal. Each and every question from the NCERT Textbook is answered in a systematic format to help students learn in a shorter duration. In reality, the two questions have answers, which are complex numbers. = a 5. Example: Simplifying √20. Either name can be used, and both names mean the same thing. Mark Lundstrom Purdue University. Determine the intercepts of the plane intersecting the xyz coordinate. Answers are in video format. Aug 14, 2021 · This will help us to solve the problems of indices. 2. ( hkl) – for single plane and {hkl} for a group of planes. It is a Indices provide a compact algebraic notation for repeated multiplication. Simplify \(p^3 \div p^{6}\) Solution. (7. The law for multiplying is `2^m xx 2^n = 2^((m+n))` There is a similar law for dividing: `4^5 ÷ 4^3` `= frac(4xx4xx4xx4xx4)(4xx4xx4)` `= 4 xx4 = 4^2` and in this case the same answer is obtained by subtracting the indices. 3) (xy) n = x n y n. In this case the numerator is 1 so the answer stays the same. Document Description: Surds & Indices - Introduction and Examples (with Solutions) for Banking Exams 2024 is part of Quantitative Aptitude for Competitive Examinations preparation. A collection of videos, activities and worksheets that are suitable for A Level Maths. Test your knowledge by diving into some example questions. In order to master the techniques explained here it is 4 3 is the index form (or power form) of 64; 4 × 4 × 4 is the expanded form of 64; For 64 = 4 × 4 × 4 = 4 3, the base number 4 appears three times as a factor of the basic numeral (or number) 64; 4 3 is read as '4 to the power 3' or simply '4 cubed' Example 2. This law states that when you divide two terms with the same base, you subtract the exponents. This will help the students in understanding the chapter more clearly. Some of the most common are: Air (gas on gas). PI = 1. So if we can write the two bases, 2 and 4, with the same base, the only difference in the two sides will be their powers. Thus, if the index of any non-zero number is 0, then the value will be 1. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. Scroll down the page for more examples and solutions on how to use the rules of indices. Jul 8, 2024 · Binomial Surd: when two surds give rise to one single surd, the resultant surd is known as binomial surds. MATH 2901. Textbook page references. or indicial or subscript or suffix notation. 8√x6y2 Rewrite the root 8 as a rational exponent (x6y2)1 8 Multiply exponents x6 8y2 8 Reduce each exponent fraction x3 4y1 4 All exponents have denominator 4, rewrite in Sep 24, 2021 · Worked examples of algebraic indices. Solution: Math Worksheets. Thus the simplificiation 2 5 × 2 3 = 2 8 quickly leads Sep 2, 2019 · Previous: Distance Time Graphs Practice Questions Next: Negative Indices Practice Questions GCSE Revision Cards Example – 12. Practise. mc-TY-indicespowers-2009-1. Some concepts appear at the lower end of GCSE higher papers and should only serve as a brief recap. 31. Solution: Let us first do the general case: what is the greatest term in the expansion of \({(1 + x)^n}\) , where n is an arbitrary rational number. Indices are designed to represent, or track, a particular industry or market. Example 1: Example 2: Example 3: Logarithms. Example question calculating CPI and inflation. The topics in the chapter include. Finding rate of change. 4) In the section we will be looking at indices or powers. Recall the formula for MCH and MCHC – the RBC and Hct are the denominator; so, they are inversely proportional to MCH and MCHC respectively. We've selected the essential questions on Laws of Indices so you can identify difficulties and work on them. It is called as “a to the power of 3”. Keep track of what you've done and what you still need to cover for free! Create an Account. 4 3 ÷ 4. Math. Subscribe Now to get Full Access to ALL this Subject's Topics and Quizzes for this Term! Click on the button "Subscribe Now" below for Full Access! Mar 22, 2024 · Figure 22. Maths : Indices - Introduction Indices or powers are used to write statements involving repeated multiplication in shorthand. Also, read: Index Dec 12, 2018 · Explanation of Miller indices problems #solidstate #Rqphysics Mar 22, 2023 · column_num - is the column number from which to return a value. Our consistent goal has been to present the chapters, examples, and questions in a clear and engaging way so that students will be motivated to “learn” and “understand” math. Laws of Indices. You can return the answer in any order. Find the value of a and the value of n . 1)View SolutionHelpful TutorialsRational (fractional) indicesSummary of indices 2)View SolutionHelpful TutorialsRational […] Apr 21, 2021 · Profitability Index Calculation Example #1 Let’s stick with the same Projects A and B that we saw earlier in this article, with the NPV of £10,000 for Project A, and £100,000 for Project B. For example, 1 0 = 1, 7 0 = 1. For example, we can see that the project 3 in above example has a negative cash flow of $10,000 on date 1 (C 1). In this section of text you will learn about powers and rules for manipulating them through a number of worked examples. Enter the reference containing the lookup value to be returned. For example: a 3 is a number with an index of 3 and base ‘a’. Flip and change the power -2 to +2. A-Level Maths Edexcel C1 June 2009 Q9a. But, remember that 0 0 ≠ 1. 3. What was the inflation rate between 2016 and 2017? Example: Hyperlipidemia and Leukocytosis. 2 Raise the answer to the power of the numerator. Scroll down the page for more examples and solutions for dividing exponents. Negative Indices 6. It is used to gauge inflation and changes in the cost of living. Examples. Simplify. Solutions. This law states that when you multiply two terms with the same base, you add the exponents. Surds are the root values that cannot be written as whole numbers. Often, more than one rule has to be used when simplifying expressions with indices. × ×. 5-z. Class 9 Chapter 8 Indices ML Aggarwal Solutions for ICSE is one of the most important chapter for the board exams which is based on simplyfying equations and finding values. Find the magnitude of the greatest term in the expansion of \({\left( {1 - 5y} \right)^{ - 2/7}}\) for \(y = \begin{align}\frac{1}{8}\end{align}\) . 5. This coordinate system can indicate directions or planes, and are often written as (hkl). 1) The laws of indices and surds are to be remembered to solve problems on surds and indices. 3 are scalars, called the Cartesian components or coordinates of a. If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable. Solutions of all exercise questions, examples, miscellaneous exercise, supplementary exercise are given in an easy to understand wayThe chapters and the topics in them areChapter 1 Relation and Functions– Types of Relation - Reflexive, Symmetr. Autoagglutination → ↓ RBC and Hct → It primarily affects the RBC and Hct (falsely decrease). This value can be written as: √3 3 = (3 3) ½ = 3 3/2 Where 3/2 is the index. Multiplying and dividing indices, raising indices to a power and using standard form are Aug 11, 2023 · An index is a tool used to track the performance of a group of financial assets. Indices are the power or exponent of a value. Example 1: fractional Indices where the numerator is 1. Download Chapter-wise NCERT Solutions for Class 12 Chemistry. Aug 11, 2023 · An index is a tool used to track the performance of a group of financial assets. So . = INDEX (E1:E10. On completion of this TLP you should: Understand the concept of a lattice plane; Be able to determine the Miller indices of a plane from its intercepts with the edges of the unit cell; Be able to visualise and draw a plane when given its Miller indices; Be aware of how knowledge of lattice planes and their Miller indices Oct 25, 2021 · The list of important index laws is given here in the shareable image format, kindly make use of it for quick reference before exams and memorize the laws frequently. zf ka ny ie vb ar yr yt gc if