Rules of Powers

This page will deal with operations involving exponents. The properties discussed require that the bases be the same unless otherwise stated.

Basics of Exponents

Exponents are written in the form of:

an

"a" is called the base while "n" is the exponent

The exponent tells how many times the base is being multiplied by itself.

For more information go to The Use of Exponents

Exponents is a more simple way of writing repeated multiplication.

Repeated Multiplication                                      Exponential Form

a * a * a * a                                                                a4

(2x) (2x) (2x) (2x)                                                                                  (2x)4

Multiplying with Exponents

When multiplying two numbers that have exponents simply add the exponents.

For example: a4 * b6 = ab(4+6) = a10

Dividing with Exponents

When dividing simply subtract the exponents.

For example: a4/b2= a/b(4-2) = a/b2

When a base, lets say a, is being taken to the power of m and that is in parentheses and outside the parentheses is the power of n. (am)n. m and n can be multiplied together and A can be taken to the power of m times n.

For example: (a5)3=a5*3=a15

If a is being taken to a negative power you could put it on the bottom of a fraction so the power would become positive. a-1 = 1/a1 = 1/a

For example: a-3= 1/a3

Basic Rules of Exponents