Show WorkingWorked example 1: squares, cubes and roots
Work out 42.
- 42 means 4 × 4.
- 4 × 4 = 16.
Answer 16
NumberFoundation and Higher (some Higher only)
Powers and roots GCSE questions with answers
8 powers and roots questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.
Powers and roots questions cover squares, cubes, square roots, cube roots and what a negative power means. On Higher you also work out fractional and negative indices, such as 64^(−1/3).
01 / Quiz yourselfTry it, then tap to check
Powers and roots questions to try
Work each one out on paper first. Then open the answer and compare your working with ours, step by step.
01 / Squares, cubes and rootsBoth tiers
Work out 92.
Show the answer and working
- 92 means 9 × 9.
- 9 × 9 = 81.
Answer 81
02 / Squares, cubes and rootsBoth tiers
Work out 152.
Show the answer and working
- 152 means 15 × 15.
- 15 × 15 = 225.
Answer 225
03 / Squares, cubes and rootsBoth tiers
Work out the cube root of 1000.
Show the answer and working
- The cube root of 1000 is the number that you multiply by itself three times to make 1000.
- 10 × 10 × 10 = 1000, so the cube root of 1000 is 10.
Answer 10
04 / Negative powersBoth tiers
Work out the value of 10−1. Give your answer as a decimal or a fraction.
Show the answer and working
- A negative power means "one over" the same positive power.
- 10−1 = 1101 = 110 = 0.1.
Answer 0.1
05 / Negative powersBoth tiers
Work out the value of 3−4.
Show the answer and working
- A negative power means "one over" the same positive power.
- 3−4 = 134 = 181.
Answer 181
06 / Negative powersBoth tiers
Work out the value of 5−1.
Show the answer and working
- A negative power means "one over" the same positive power.
- 5−1 = 151 = 15.
Answer 15
07 / Negative and fractional indicesHigher only
Work out 6443. Give your answer as an exact value.
Show the answer and working
- Do the root first to keep the numbers small. The bottom of the power, 3, means the cube root. The cube root of 64 is 4.
- The top of the power, 4, means raise it to the power 4: 44 = 256.
- So 6443 = 256.
Answer 256
08 / Negative and fractional indicesHigher only
Work out 3−2. Give your answer as an exact value.
Show the answer and working
- A negative power means 1 over the positive power: 3−2 = 132.
- 32 = 3 × 3 = 9.
- So 3−2 = 19.
Answer 19
02 / What's covered3 kinds of question
Powers and roots at GCSE and where marks go
- Squares, cubes and rootsBoth tiers
- Negative powersBoth tiers
- Negative and fractional indicesHigher only
Worked example 2: negative and fractional indices
Work out 3215. Give your answer as an exact value.
- A power of 15 means the fifth root.
- 2 × 2 × 2 × 2 × 2 = 32, so the fifth root of 32 is 2.
Answer 2
A common mistake
Thinking a negative power makes the answer negative. A negative power means one over the number, so 10^−2 = 1/10² = 1/100 = 0.01.
03 / Practise itiPhone and iPad
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