# Exponents and Powers

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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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