Exponents are operations to do:

3² means multiply 3 by itself 2 times = (3) (3) = 9

3^-1 means to take the reciprocal of 3 =

Example 1

Example 2

Any non-zero number raised to the zero power equals 1.

a0 = 1 for a does not equal 0. 30 = 1

(9x)0 = 1 9x0 = 9 . x0 = 9 . 1 = 9

Example 3

When multiplying the same base: keep the base and add the exponents.

aman = am+n

1. a⁷a⁵ = a⁷⁺⁵ = a¹²

2. a⁹a^-3 = a^9+(-3) = a⁶

3. x⁵x^-7 = x^5+(-7) = x^-2 =

Example 4

When dividing the same base: keep the base and subtract the exponents. This is the same as reducing a fraction.

Example 5

When raising a power to a power: multiply the exponents.

(am)n = amn

1. (a⁵)³ = a^{(5) (3)} = a¹⁵

2.

Example 6

Exponents distribute across multiplication and division (NOT across addition and subtraction).

(ab)n = anbn

3. (x + 3)2	= (x + 3) (x + 3)
	= x2 + 3x + 3x + 9
	= x2 + 6x + 9

Example 7

A negative exponent represents a reciprocal. Remove a negative in the exponent by taking the reciprocal. In a product or quotient, that means moving the base and exponent from the numerator to the denominator or vice-versa, changing the sign in the exponent.

Example 8

Exponents only apply to a single character unless there are parentheses.