Recall what the power means: 9^2 Write it out in full: 9^2 = 9 × 9 Multiply the final factor: 9 × 9 = 81 Answer: 81

Recall what the power means: 12^2 Write it out in full: 12^2 = 12 × 12 Multiply the final factor: 12 × 12 = 144 Answer: 144

Recall what the power means: 4^3 Write it out in full: 4^3 = 4 × 4 × 4 Multiply the next factor: 4 × 4 = 16 Multiply the final factor: 16 × 4 = 64 Answer: 64

Powers and roots Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Powers and roots questions. See exactly how to solve problems on squares, cubes, square roots, cube roots.

squarescubessquare rootscube rootspowers of 2powers of 3

GCSE Foundation70 questionsStep-by-step solutions

Question 1

1 markeasy

Work out

7

squared, that is

7^2

Worked solution

Recall what the power means
$7^2$
A power tells you how many times to multiply the base by itself, so this means $7$ multiplied $2$ times.
Write it out in full
$7^2 = 7 \times 7$
Writing every factor out makes the repeated multiplication clear.
Multiply the final factor
$7 \times 7 = 49$
Multiply $7$ by the last $7$ , giving $49$ .

Answer

49

Question 2

1 markeasy

Work out

9^2

Worked solution

Recall what the power means
$9^2$
A power tells you how many times to multiply the base by itself, so this means $9$ multiplied $2$ times.
Write it out in full
$9^2 = 9 \times 9$
Writing every factor out makes the repeated multiplication clear.
Multiply the final factor
$9 \times 9 = 81$
Multiply $9$ by the last $9$ , giving $81$ .

Answer

81

Question 3

1 markeasy

Work out

12^2

Worked solution

Recall what the power means
$12^2$
A power tells you how many times to multiply the base by itself, so this means $12$ multiplied $2$ times.
Write it out in full
$12^2 = 12 \times 12$
Writing every factor out makes the repeated multiplication clear.
Multiply the final factor
$12 \times 12 = 144$
Multiply $12$ by the last $12$ , giving $144$ .

Answer

144

Question 4

1 markeasy

Work out

3

cubed, that is

3^3

Worked solution

Recall what the power means
$3^3$
A power tells you how many times to multiply the base by itself, so this means $3$ multiplied $3$ times.
Write it out in full
$3^3 = 3 \times 3 \times 3$
Writing every factor out makes the repeated multiplication clear.
Multiply the next factor
$3 \times 3 = 9$
Multiply the running total $3$ by another $3$ to get $9$ .
Multiply the final factor
$9 \times 3 = 27$
Multiply $9$ by the last $3$ , giving $27$ .

Answer

27

Question 5

1 markeasy

Work out

4^3

Worked solution

Recall what the power means
$4^3$
A power tells you how many times to multiply the base by itself, so this means $4$ multiplied $3$ times.
Write it out in full
$4^3 = 4 \times 4 \times 4$
Writing every factor out makes the repeated multiplication clear.
Multiply the next factor
$4 \times 4 = 16$
Multiply the running total $4$ by another $4$ to get $16$ .
Multiply the final factor
$16 \times 4 = 64$
Multiply $16$ by the last $4$ , giving $64$ .

Answer

64

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