Exponent Rules (Partial)

Negative Exponents

100

(-6)^-2

1/6²

200

1/3^-2

3²

300

8^-3

1/8³

400

5b^-4

5/b⁴

500

(-y)^-2

1/(-y)²

Zero Exponents

100

5⁰

1

200

9x⁰

9

300

6(x+y)⁰

6

400

4x⁰y⁰z⁴

4z⁴

500

x⁰+y⁰+z⁰

3

Product Rule

100

6³ * 6²

6⁵

200

5(5²)

5³

300

(5⁶)(5)

5⁷

400

(xy)(x⁵y⁸)

x⁶y⁹

500

(x³y²)(x³y²)*(x²)(x²)

x¹⁰y⁴

Evaluate (Solve)

100

2²

4

200

10⁵

100,000

300

5³

125

400

3³ * 3⁴

3⁷ -->2,187

500

8^-4

1/8⁴ --> 1/4,096

Concepts & Vocab

100

what is the big number called --> 5²

base

200

What is the little number called --> 5²

exponent

300

What is the answer to all 0 exponent problems? 

ex: 10⁰

always 1

400

what is the rule for multiplying with exponents when the bases match?

ex: 5² * 5⁹

add the exponents together

ex: 5¹¹

500

what is the rule to turn negative exponents positive?

ex: 5^-5

turn it into a fraction with 1 on top and the exponent on the bottom. (If you can solve the exponent solve it!)

ex: 1/5⁵ -->1/3,125