Exponents & Roots Practice
Practise squares, powers and square roots — the shorthand for repeated multiplication.
Grades 6–8 · 6.EE⚡ Middle school
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How exponents and roots work
An exponent tells you how many times to multiply a number by itself. A square root asks the reverse question.
- Power: 24 means 2 × 2 × 2 × 2 = 16.
- Square: a number to the power 2 — 52 = 25.
- Square root: √25 asks “what times itself is 25?” — the answer is 5.
Worked examples
A power33 = 3 × 3 × 3 = 27.
A square root√81 = 9, because 9 × 9 = 81.
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Tips & common mistakes
- Multiplying the base by the exponent (32 is 9, not 6).
- Forgetting that a square root undoes a square.
- Mixing up which number is the base and which is the exponent.
Frequently asked questions
What is an exponent?
A small raised number showing how many times to multiply the base by itself — 23 = 2 × 2 × 2 = 8.
What is a square root?
The number that, multiplied by itself, gives the value under the root — √49 = 7 because 7 × 7 = 49.
What’s the difference between 32 and 3 × 2?
32 means 3 × 3 = 9; 3 × 2 is just 6. The exponent means repeated multiplication, not doubling.
What is a perfect square?
A number that is some whole number squared — 1, 4, 9, 16, 25 and so on. Their square roots are whole numbers.
What grade are exponents taught in?
Whole-number exponents start in grade 6 and develop through grade 8.