Indices II — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)When multiplying powers of the same base, add the indices.

x⁸

Question 2

(a)Square both the coefficient and the power: 2² = 4, and (x³)² = x⁶.

4x⁶

Question 3

(a)Write 32 as a power of 2: 32 = 2⁵, so the indices must be equal.

x = 5

Question 4

(a)Subtract the indices when dividing powers of the same base.

x⁴

Question 5

(a)Cube the coefficient and multiply the power by 3: 3³=27, (x²)³=x⁶.

27x⁶

Question 6

(a)Write 81 as a power of 3: 81 = 3⁴, so 2x = 4.

x = 2

Question 7

(a)Square inside the bracket first: x⁶y⁴, then divide by x².

x⁴y⁴

Question 8

(a)Any non-zero number to the power 0 equals 1.

Question 9

(a)Add the indices: 1/2 + 3/2 = 2.

x²

Question 10

(a)Square first: 4x⁶, then divide by 4x².

x⁴

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