Exponent Properties

Same Base (Product of Powers Property)

100

Simplify: 5² x 5⁷

5⁹

200

Simplify: 1¹⁰ x 1¹

1¹¹

300

Simplify: 12^-2 x 12⁵

12³

400

Simplify: 4² x 4³ x 4²

4⁷

Same Exponent (Power of Products Property)

100

Simplify: 2³ x 4³ 

8³

^{(2 x 4)3}

200

Simplify: 5⁷ x 2⁷

10⁷

(5 x 2)⁷

300

Simplify: 1⁸ x 2⁸ x 4⁸

8⁸

(1 x 2 x 4)⁸

400

True or False: (5 x 11)^{4 =} 5⁴ + 11⁴

False

(5 x 11)^{4 =} 5⁴ x 11⁴

Power of Powers Property

100

Simplify: (10⁵)⁴

10²⁰

200

Simplify: (1⁹)¹

1⁹

300

Simplify: (11⁴)¹¹

11⁴⁴

400

Simplify: (2³5¹)²

2⁶5²

Quotient of Powers Property

100

Simplify: 2⁵ / 2¹

2⁴

200

Simplify: 8⁷ / 8⁴

8³

300

Simplify: 3² / 3⁵

3^-3

400

Write down the property rules for solving Quotient Powers.

When dividing two exponential expressions with the same base, subtract the exponents and keep the base.

Exiled by Exponents

100

What would make this statement true?

8^? x 8⁶ = 8¹⁰

? = 4

200

What would make this statement true?

(5³)^? = 5²⁴

? = 4