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. Laws of indices powers a powerpoint resource that introduces the laws of indices. Indices provide a compact algebraic notation for repeated multiplication. Indices or powers a knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. Exponential notatio n is a power ful way to express repeated multiplication of the same number. Decode the puzzle to practice the laws of indices when raising a power to another power, includes multiplying and dividing indices. 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.
Without a calculator, use the laws of indices to help you evaluate the following. Before using standard form, we revise multiplying and dividing by powers of 10. To see how to deal with fractional powers consider the following. Click to read more about indices and download our comprehensive gcse maths study guide.
Index is used to show that a number is repeatedly multiplied by itself. Key point an index, or power, is used to show that a quantity is repeatedly multiplied by itself. Indices or powers gcse maths study guide revision material. There are a number of important rules of index numbers. Literacy activities find a word study stack quizlet crossword fill in the blanks. Aqa, ocr, edexcel gcse maths indices and powers questions name. Laws of indices this worksheet has questions about the laws of indices. Positive exponents indicate the number of times a term is to be. The a represents the number and n and m represent the powers. Includes small investigations and mini plenaries to get the pupils thinking. A rational number is one that can be expressed as a fraction, where a and b are integers. Facility with the arithmetic of integers and fractions. The index laws apply to fractional indices as well as positive and negative integer indices.
Surds and indices shortcuts, tricks, pdf and formulas. For example, is it much easier to write 3 5 than 3. An index is a power of numbers that indicate how many times it has been multiplied by itself. Surds and indices aptitude test, questions, shortcuts. Selection file type icon file name description size revision time user. Multiplying and dividing indices, raising indices to a power and using standard form are explained.
For example, 2 5 means that you have to multiply 2 by itself five times 2. Surds and indices points to remember page 2 surds and indices examples page 3 surds and indices important questions page 5. The cubed sign tells us to take the number and multiply it by itself 3 times. Algebra uses symbols or letters to represent quantities. Indices or powers, or exponents are very useful in mathematics. Exponents are also called powers or indices the exponent of a number says how many times to use the number in a multiplication. To manipulate math expressions, we can consider using the law of indices. 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 reasoning behind the index laws is straightforward. The print activity may be opened in word format instead of pdf so that changes to questions can be made.
Use the rules of indices to simplify each of the following and where possible evaluate. Indices practice questions evaluate the following expressions without your calculator. The 48 laws of power by robert greene penguin books 2000 hardcover edition isbn 0670881465 paperback edition isbn 0 14 02. Indices provide a way of writing numbers in a more convenient form. Laws of indices this guide describes how to work with and manipulate the laws of indices in mathematics. 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. Change each expression into base of 3 or 5 before applying the laws of indices and decode the puzzle. Use the product law in the explore it mode for the following exercise. The power, also known as the index, tells you how many times you have to multiply the number by itself. An integer is a whole number positive, negative or zero. In the example, underneath, you will see that x to the power of 0 is always equal to 1. 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. If you like this resource, search for index laws 1, 2 and 4. 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.
This section covers indices and the uses of indices in algebra. In english, when a letter is smaller and on the upper right side of the bigger letter, we call it a superscript. Indices are also known as powers, exponents or sometimes even orders. Taking a power is simply a case of repeated multiplication of a number with itself while taking a root is just equivalent to. Indices show how many times a number or letter has been multiplied by itself. To divide when two bases are the same, write the base and subtract the exponents. Index notationpowers doingmaths free maths worksheets. In this section of text you will learn about powers and rules for manipulating them through a number of worked examples. Let n be a positive integer and a be a real number, then. Indices usually appear in mathematics as a numerical superscript after a number or variable and are also known as powers or exponents. To multiply when two bases are the same, write the base and add the exponents. 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. In english, when a letter is smaller and on the upper right side of the bigger letter, we call it.
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. This video shows an animated guide to indices for higher tier exams. We add the indices when we multiply two powers of the same number. Positive exponents indicate the number of times a term is to be multiplied by itself. Laws of indices give rules for simplifying calculations or expressions involving powers of the same base. I is used to stand for interest, p for principle, r for rate, and t for.
The tutor2u maths team comprise experienced gcse and a level maths teachers and examiners with wide experience of all the main exam. Writing in index form, multiplication of indices and division of indices. In other words, in our example if the exponent 2 was a 1, simplified the example would then be 4. 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. On completion of this tutorial you should be able to do the following. Power, indices and surds tips and tricks governmentadda. Specifically, powers of 10 express very large and very small numbers in a manner which is convenient to read, write and compare.
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. It is called as a to the power of 3 quick tips and tricks. Here a is called the base and m is the index, power or exponent. Indices refers to the power to which a number is raised. If the powerexponent of a number is 1, the number will always equal itself.
Worked examples on indices and logarithms questions and answers on indices and logarithms. The laws of indices introduction a power, or an index, is used to write a product of numbers very compactly. There is another rule with regards to indices that originates from law 2. Knowledge of the index laws for positive integer powers. Index laws 3 raise a power to a power teaching resources. The concepts relating to indices are relatively easy to explain from first principles. It is compulsory that question will comes from this topic. Expressions with the same base, can be manipulated using the law of indices. In the expression above, you can see that x to the power of 0 is equal to one. 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. An index number is a number which is raised to a power. The first three laws above x1 x, x0 1 and x1 1x are just part of the natural sequence of exponents. When the power is 2 we say squared, when the power is 3 we say cubed and for all other powers. 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.
The first law of indices tells us that when multiplying two identical numbers together that have different powers eg. Covers laws of indices including fractional and negative indices, solving equations involving indices igcse fm syllabus and raising a single term to a power. Familiarity with rounding numbers correct to a given number of decimal places. Ppt laws of indices powerpoint presentation free to. This worksheet includes multiply and dividing powers, and finding the power of a power.
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. Indices also known as powers or exponents studywell. Maths made easy complete tuition ltd 2017 rules of indices powers 1. Using an index or power laws of indices bbc bitesize. Displaying all worksheets related to laws of indices. This rule states that anything to the power of 0 is equal to 1. This topic are very useful and acts as the base of simplification and algebra. 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. There are three rules that should be used when working with indices. For any nonzero integer a, am 1 am laws of exponents are a a m.