Index Laws

Index Law 1

100

a^m x aⁿ = 

a^m+n

200

3² x 3⁴ = 

3⁶

300

5⁹ x 5⁸ = 

5¹⁷

400

5² x 5³ x 2⁴ x 2⁵ = 

5⁵ x 2⁹

500

2a³ x 3a⁴ x 2b² x b² =

8a⁷b⁴

Index Law 2

100

a^m ÷ aⁿ = 

a^m-n

200

4⁵ ÷ 4² =

4³

300

6¹² ÷ 6⁸ = 

6⁴

400

4⁴ ÷ 4² ÷ 3⁶÷ 3³ = 

4²÷ 3³

500

4a⁴÷ 2a² =

2a²

Index Law 3

100

a⁰ =

1

200

(-5)⁰ =

1

300

3(x⁵)⁰ = 

3

400

y⁰ + 2 =

3

500

5a⁰ -(8y)⁰

4

Index Law 4

100

(a^m)ⁿ =

a^{m x n}

200

(a³)² = 

a⁶

300

(4³)⁴ = 

4¹²

400

(2a²)³ = 

8a⁶

500

(3b²)² = 

9b⁴

Random

100

Expand 4³

 

4 x 4 x 4

200

Write in index form:
a x a x a x a x a

a⁵

300

Evaluate (-2)³

-8

400

Find the value of m in:

3⁵ x 3^m = 3⁷

m= 2

500

If (4ⁿ)^m=4¹⁶ and n = 2, what is the value of m?

m = 8