The laws of indices

Question 1

Simplify w³ x w¹¹

Answer 1

w¹⁴

(add the powers in a multiplication if the base letter is the same)

Question 2

Simplify (y²)⁵

Answer 2

y¹⁰

(multiply the powers)

Question 3

Simplify (5d³)²

Answer 3

25d⁶

(multiply the powers; 25 is 5²)

Question 4

Simplify p⁴ x p

Answer 4

p⁵

(add the powers in a multiplication if the base letter is the same; p is p¹)

Question 5

Simplify (2a⁴)³

Answer 5

8a¹²

(multiply the powers; 8 is 2³)

Question 6

Simplify t² x t⁵

Answer 6

t⁷

(add the powers in a multiplication if the base letter is the same)

Question 7

Simplify 3k⁵ x 4k²

Answer 7

12k⁷

(add the POWERS in a multiplication if the base letter is the same, but times 3 by 4)

Question 8

Simplify 5w² x 2w⁶

Answer 8

10w⁸

(add the POWERS in a multiplication if the base letter is the same, but times 5 by 2)

Question 9

Simplify t⁷ ÷ t³

Answer 9

t⁴

(subtract the powers in a division if the base letter is the same)

Question 10

Simplify (x⁷)²

Answer 10

x¹⁴

(multiply the powers)

Question 11

Simplify 12t⁶ ÷ 6t

Answer 11

2t⁵

(subtract the POWERS in a division if the base letter is the same, but divide 12 by 6; t is t¹)

Question 12

Simplify (d³)⁴

Answer 12

d¹²

(multiply the powers)

Question 13

Simplify w⁸ ÷ t²

Answer 13

w⁶

(subtract the powers in a division if the base letter is the same)

Question 14

Simplify p⁵ ÷ p

Answer 14

p⁴

(subtract the powers in a division if the base letter is the same; p is p¹)

Question 15

Simplify 10p⁷ ÷ 2p⁴

Answer 15

5p³

(subtract the POWERS in a division if the base letter is the same, but divide 10 by 2)