Index Laws

Multiplying Indices

100

y³ x y⁵

y⁸

200

a⁵ x a^-3

a²

300

p^-4 x p⁹ 

p⁵

400

3m⁴ x 3m⁷

9m¹¹

500

5m³ x 5m²

25m⁵

Dividing Indices

100

5¹² divided by 5⁴ 

5⁸

200

7⁴ divided by 7⁵

7^-1

300

24x²y

^_______

8xy

  3x

400

35a³b⁴

^_______

-7a⁴b⁵

-5

____

ab

500

32m³n⁵

^________

80m³n⁶

 2

___

5n

Raising Powers

100

(x³)²

x⁶

200

(p⁴)¹⁰

p⁴⁰

300

(d⁵)^-3

d^-15

400

(p²m⁴)⁵

p¹⁰m²⁰

500

(4y¹⁰)²

16y²⁰

Zero Indices

100

-4 x (7m)⁰

-4

200

134 x (52m)⁰

134

300

5n⁰ + (4n)⁰

5 x 1 + 1 = 6 

400

4a⁰ + 3

7 

500

a⁰-1

0

Mixed Questions

100

(2a⁷bc³)⁴

16a²⁸b⁴c¹²

200

5y^-3x3y⁷

15y⁴

300

3a⁸ + 3a⁴ x 5a⁴ 

______________

(3a⁴)³

2

__

3a⁴

400

(2m²)² + 3m³ x 2m

________________

           4m⁵

 5

___

2m

500

(2z²)³ - 2z² x 3z⁴

^{___________________}

          (3z)² 

2z⁶

_____

9z²

2z⁴

^___

 9