Index Laws Revision

Multiplication

100

Simplify the following:

2³  x  2⁵

2⁸

200

Simplify the following: 

19⁵  x  19⁷

19¹²

300

Simplify the following: 

2⁷ x 2⁸ x 2 x 2⁶

2²²

400

Simplify the following: 

9³ x 9² x 6⁸ x 9² x 6⁹ x 6

9⁷ x 6¹⁸

500

Simplify the following:

8² x 11⁵ x 8⁸ x 11¹³ x 11 x 8⁶⁴

8⁷⁴ x 11¹⁹

Division

100

Simplify the following:

8¹⁸ ÷ 8⁵

8¹³

200

Simplify the following: 

4¹²/4⁶

4⁶

300

Simplify the following

13¹³ ÷ 13²  – 11²¹ ÷ 11

13¹¹ - 11²⁰

400

Simplify the following: 

27¹⁹/27¹³ x 36²⁵/36¹⁶

27⁶ - 36⁹

500

Simplify the following:

14¹⁷/14⁸ x 5¹¹/5⁶

14⁹ x 5⁵

Zero

100

9⁰ = 

1

200

652⁰ = 

1

300

9⁰ - 9⁰ = 

0

400

554 x 3214⁰ = 

554

500

576⁰ + 654⁰ + 87⁰ = 

3

Power

100

Simplify the following:

(2³)⁴

2¹²

200

Simplify the following: 

(2)¹⁸

2¹⁸

300

Simplify the following:

(4⁶ x 3⁷)⁴

4²⁴ x 3²⁸

400

Simplify the following: 

(5² ÷ 2⁶)⁸

5¹⁶ ÷ 2⁴⁸

500

(7⁵ x 2³)⁵ + (4²)⁸

7²⁵ x 2¹⁵ + 4¹⁶

Notation/ Combined

100

Express the following in index notation: 

6 x 6 x 2 x 6 x 2 x 2 x 6 x 6 x 2

6⁵ x 2⁴

200

Identify the power and the base: 

6⁸

Power = 8

Base = 6

300

Simplify the following: 

7² × 7⁴ × 8¹⁴

___________

(8⁶)²

7⁶ x 8²

400

Simplify the following: 

4³ × 4 × 2¹⁷  

_________

(2⁴ × 4²)³

4^-2 x 2⁵

500

5⁴ × 4⁴ × 5⁷ × 4²  

__________________________

(5⁴ x 4²)²

5³ x 4²