Multiplication Properties of Exponents Multiplying with Like Bases and Exponents Keep the base the same and add the exponents. Ex: 3 2  3 7 = 3 9 x 4  x 11 = x 15 x 4  x 11 = x 15

Power of a Power Property This property is used when an exponent is outside parentheses. This property is used when an exponent is outside parentheses. Keep the base the same and multiply the exponents. Keep the base the same and multiply the exponents. If your base does not have an exponent put a “1” as the exponent. If your base does not have an exponent put a “1” as the exponent. (x 2 ) 5 = x 10 (3x 3 ) 4 = (3 4 )(x 12 ) = 81x 12

Negative & Zero Exponents Zero Exponents: Any base, except 0, raised to the zero power is equal to = 1x 0 = 1 (2x) 0 = 1

Negative Exponents: 1. Move the base to the opposite location (numerator or denominator). If you clean out the numerator, you must put a 1 in the numerator slot. 2. Move the exponent along with the base and make it positive. 3. Simplify.

Division Properties of Exponents To divide powers having the same base: 1. Keep the base in the location with the highest exponent. 2. Subtract the exponents.

Exponent Rules 1. Parentheses with exponents on the outside. 2. Fix negative exponents 3. Numbers with exponents 4. Multiply numbers and add exponents 5. Reduce