# Exponents and Powers

## Exponents are useful to express very large numbers, making them shorter and hence easier to understand and compare. Exponential form is a form involving two numbers written as an , where a is called the base and n is called the exponent. Expanded form of a number means to expand a number to show the value of each digit. For a positive integer a, an implies a × a × a × ….n times, i.e. a multiplied by itself n times and an is read as ‘a raised to the power of n’. Following laws of exponents are obeyed by all numbers in exponential form: i. 1m = 1 ii. (–1)even number = 1 iii. (–1)odd number = –1 iv. a0 = 1 v. ax × ay = ax+y vi. ax ÷ ay = ax–y , x > y vii. (ax )y = ax×y viii. ay × by = (ab)y ix. ay ÷ by = (a/b)y where a and b are non-zero integers and x and y are whole numbers. A number expressed as a decimal number between 1.0 & 10.0 (including 1.0) multiplied by a power of 10 is said to be in standard form. Standard form is also known as scientific notation.

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