Heather's Math Site

Exponents

Let's start with some definitions:

The number of times a number is multiplied by itself is called an exponent.

The number/variable is called the base.

For example:

An exponent is represented like this: x⁵, where x is the base and 5 is the exponent. Sometime you will hear the 5 as a power, such as x to the power of 5. Another way will be x to the fifth power.

Note: When the exponent is a 2 or a 3 it is read as x squared and x cubed, respectively.

Laws of Exponents

Rule	Example
x¹ = x	5¹ = 5
x⁰ = 1	5⁰ = 1
x^a x^b = x^{a + b}	x² x³ = x^{2 + 3} = x⁵
x^a / x^b = x^{a - b}	x⁴ / x² = x^{4 - 2} = x²
(x^a)^b = x^ab	(x³)⁴ = x^3*4 = x¹²
(xy)^a = x^a y^a	(xy)⁵ = x⁵ y⁵
( x / y )^a	x^a / y^a
x^-a = 1 / x^a	x^-3 = 1 / x³