Laws of Exponents

Product Rule

100

x² ∙ x³

What is x⁵

200

x ∙ x²

What is x³

300

3² x 3⁸

What is 3¹⁰

400

2² x 2²⁵⁰ 

What is 2²⁵²

500

(3²)(3¹⁰⁰⁰)

What is 3¹⁰⁰²

Dividing

100

3⁴/3²

What is 3²

200

x⁴ / x²

What is x²

300

x⁹ / x²

What is x⁷

400

6⁴/6²

What is 6²

500

5³6⁴/5⁵6⁷

What is 1/5²6³

Exponent of Exponent

100

(a²)³

What is a⁶

200

(b³)⁵

What is b¹⁵

300

(2 x 7)³

What is 14³

400

(2³)²

What is 2⁶

500

(3²5⁴)²

What is 3⁴5⁸

Negative Exponents

100

x^-1

What is 1/x

200

3^-2

What is 1/3²

300

y^-1

What is 1/y or 1/y¹

400

2^-2

What is 1/2²

500

x^-4

What is 1/x⁴

Power of a Power

100

(3²)³

3⁶

200

(4 x 5)⁴

20⁴ or 4⁴ x 5⁴

300

(3³)^-2

1 / (3⁶)

400

(3⁵ x 2 / 8²)⁴

(3²⁰ x 2⁴ / 8⁸)

500

(1/3)^-2

3² or 9