1. Multiplying and Dividing Powers with Same Base Alex Drennan

2. Definitions A power is the value indicated by a base with an exponent: A power is the value indicated by a base with an exponent:ExponentBase

3. Multiplying To multiply powers with the same base, keep the base the same and add the exponents To multiply powers with the same base, keep the base the same and add the exponents a m x a n = a m+n

4. Example 1 1. 3 4 x 3 5 2. 3 4 x 3 5 = 3 4+5 3. 3 4 x 3 5 =3 9 1. Recognize same base 2. Add the exponents 3. Solve

5. Example 2 1. 2 -4 x 2 5 2. 2 -4 x 2 5 = 2 -4+5 3. 2 -4 x 2 5 = 2 1 4. 2 1 = 2 1. Recognize same base 2. Add the exponents 3. Solve 4. Any number to the first power equals itself

6. Dividing To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator a m a m-n a m a m-n anananan =

7. Example 1 1. 4 7 2. 4 7 3. 4 7 1. Recognize same base 2. Subtract the exponents 3. Solve 45454545 45454545 = 4 7-5 45454545 = 4 2

8. Example 2 1. 2 3 2. 2 3 3. 2 3 4. 2 -5 = 1 1. Recognize same base 2. Subtract the exponents 3. Solve 4. Negative exponent moved to denominator 28282828 28282828 = 2 3-8 28282828 = 2 -5 25252525