Index laws 3 raise a power to a power teaching resources. To manipulate math expressions, we can consider using the law of indices. An integer is a whole number positive, negative or zero. For example, is it much easier to write 3 5 than 3. It is compulsory that question will comes from this topic. Key point an index, or power, is used to show that a quantity is repeatedly multiplied by itself. Displaying all worksheets related to laws of indices. Index notationpowers doingmaths free maths worksheets.
Knowledge of the index laws for positive integer powers. Click to read more about indices and download our comprehensive gcse maths study guide. Indices usually appear in mathematics as a numerical superscript after a number or variable and are also known as powers or exponents. This video shows an animated guide to indices for higher tier exams. There is another rule with regards to indices that originates from law 2. Laws of indices powers a powerpoint resource that introduces the laws of indices. This worksheet includes multiply and dividing powers, and finding the power of a power. Taking a power is simply a case of repeated multiplication of a number with itself while taking a root is just equivalent to. Multiplying and dividing indices, raising indices to a power and using standard form are explained. Positive exponents indicate the number of times a term is to be multiplied by itself. When the power is 2 we say squared, when the power is 3 we say cubed and for all other powers. Laws of indices this guide describes how to work with and manipulate the laws of indices in mathematics. Indices any expression written as an is defined as the variable a raised to the power of the number n n is called a power, an index or an exponent of a e.
In other words, in our example if the exponent 2 was a 1, simplified the example would then be 4. In this section of text you will learn about powers and rules for. Indices materials required for examination items included with question papers ruler graduated in centimetres and nil millimetres, protractor, compasses, pen, hb pencil, eraser. Indices are a convenient way of writing multiplications that have many repeated terms. The tutor2u maths team comprise experienced gcse and a level maths teachers and examiners with wide experience of all the main exam. In english, when a letter is smaller and on the upper right side of the bigger letter, we call it a superscript.
We add the indices when we multiply two powers of the same number. Surds and indices aptitude test, questions, shortcuts. Worksheets are work 1 8 power laws, laws of indices work, maths learning service revision index laws mathematics, indices and surds, indices or powers, mathematics linear 1ma0 algebra indices, 3 indices and standard form mep y9 practice book a, index laws. The index laws apply to fractional indices as well as positive and negative integer indices. Join s of fellow maths teachers and students all getting the tutor2u maths teams latest resources and support delivered fresh in their inbox every morning. An index number is a number which is raised to a power. Ppt laws of indices powerpoint presentation free to. Expressions with the same base, can be manipulated using the law of indices. Decode the puzzle to practice the laws of indices when raising a power to another power, includes multiplying and dividing indices. The first three laws above x1 x, x0 1 and x1 1x are just part of the natural sequence of exponents. In the expression above, you can see that x to the power of 0 is equal to one. Selection file type icon file name description size revision time user. We can see that b 2 x b 5 b 7 simply by writing out the expressions in full ie b x b x b x b x b x b x b.
The cubed sign tells us to take the number and multiply it by itself 3 times. In english, when a letter is smaller and on the upper right side of the bigger letter, we call it. The print activity may be opened in word format instead of pdf so that changes to questions can be made. Laws of indices this worksheet has questions about the laws of indices. For example, 2 5 means that you have to multiply 2 by itself five times 2. In the example, underneath, you will see that x to the power of 0 is always equal to 1. The 48 laws of power by robert greene penguin books 2000 hardcover edition isbn 0670881465 paperback edition isbn 0 14 02. There are three rules that should be used when working with indices. Laws of indices give rules for simplifying calculations or expressions involving powers of the same base. Familiarity with rounding numbers correct to a given number of decimal places. Use the product law in the explore it mode for the following exercise.
To see how to deal with fractional powers consider the following. Taking a power is simply a case of repeated multiplication of a number with itself while taking a root is just equivalent to taking a fractional power of the number. Positive exponents indicate the number of times a term is to be. Change each expression into base of 3 or 5 before applying the laws of indices and decode the puzzle.
Indices provide a compact algebraic notation for repeated multiplication. Indices refers to the power to which a number is raised. In this section of text you will learn about powers and rules for manipulating them through a number of worked examples. There are a number of important rules of index numbers. For any nonzero integer a, am 1 am laws of exponents are a a m.
Dec 31, 2014 the concepts relating to indices are relatively easy to explain from first principles. This topic are very useful and acts as the base of simplification and algebra. Here a is called the base and m is the index, power or exponent. To multiply when two bases are the same, write the base and add the exponents. Covers laws of indices including fractional and negative indices, solving equations involving indices igcse fm syllabus and raising a single term to a power. Indices or powers a knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. Using an index or power laws of indices bbc bitesize.
Facility with the arithmetic of integers and fractions. Laws of indices, exponents indices are a convenient tool in mathematics to compactly denote the process of taking a power or a root of a number. Indices are also known as powers, exponents or sometimes even orders. The problem of developing a definition that adequately assesses power quality pq levels in the presence of distributed generation dg is addressed by using proper probabilistic indices for. I is used to stand for interest, p for principle, r for rate, and t for. Indices provide a way of writing numbers in a more convenient form. It is called as a to the power of 3 quick tips and tricks.
Writing in index form, multiplication of indices and division of indices. This section covers indices and the uses of indices in algebra. An index is a power of numbers that indicate how many times it has been multiplied by itself. Maths made easy complete tuition ltd 2017 rules of indices powers 1. To divide when two bases are the same, write the base and subtract the exponents. When the power is 2 we say squared, when the power is 3 we say cubed and for all other powers we say to the power of. Surds and indices points to remember page 2 surds and indices examples page 3 surds and indices important questions page 5. The problem of developing a definition that adequately assesses powerquality pq levels in the presence of distributed generation dg is addressed by using proper probabilistic indices for.
Before using standard form, we revise multiplying and dividing by powers of 10. In this leaflet we remind you of how this is done, and state a number of rules, or laws, which can be used to simplify expressions involving indices. Includes small investigations and mini plenaries to get the pupils thinking. Use the rules of indices to simplify each of the following and where possible evaluate. Aqa, ocr, edexcel gcse maths indices and powers questions name. This rule states that anything to the power of 0 is equal to 1. Indices practice questions evaluate the following expressions without your calculator. Worked examples on indices and logarithms questions and answers on indices and logarithms.
A rational number is one that can be expressed as a fraction, where a and b are integers. Power, indices and surds tips and tricks governmentadda. Indices or powers gcse maths study guide revision material. Without a calculator, use the laws of indices to help you evaluate the following. Literacy activities find a word study stack quizlet crossword fill in the blanks. Surds and indices shortcuts, tricks, pdf and formulas. Tutorial 5 indices, logarithms and function this is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals. Exponents are also called powers or indices the exponent of a number says how many times to use the number in a multiplication. The power, also known as the index, tells you how many times you have to multiply the number by itself. Indices show how many times a number or letter has been multiplied by itself. The report develops the case for a consistent set of power quality indices and objectives that can be seen as the outer envelope of performance for each power quality parameter. Let n be a positive integer and a be a real number, then. The concepts relating to indices are relatively easy to explain from first principles. If you like this resource, search for index laws 1, 2 and 4.
Specifically, powers of 10 express very large and very small numbers in a manner which is convenient to read, write and compare. Exponential notatio n is a power ful way to express repeated multiplication of the same number. Algebra uses symbols or letters to represent quantities. On completion of this tutorial you should be able to do the following. The a represents the number and n and m represent the powers. These laws only apply to expressions with the same base, for example, 3 4 and 3 2 can be manipulated using the law of indices, but we cannot use the law of indices to manipulate the expressions 4 5 and 9 7 as their base differs their bases are 4 and 9, respectively.
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