Key Stage 3 (KS3) · Mathematics

Indices, Powers and Roots: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Indices, Powers and Roots.

10 questions21 marksFree, no account

Question 1

1 mark

Find the value of \( \sqrt[3]{216} + 5^2 - \sqrt{49} \).

Question 2

1 mark

Find the value of \( \sqrt{144} - 2^3 + \sqrt[3]{27} \).

Question 3

1 mark

Simplify the expression \( (3x^2y^3)^3 \).

Question 4

1 mark

Evaluate \( \frac{2^5 \times 2^3}{2^4} \) and leave your answer in index form.

Question 5

1 mark

Calculate the value of \( 4^3 - \sqrt{81} + \sqrt[3]{125} \).

Question 6

2 marks

Evaluate the value of \( \sqrt{196} - \sqrt[3]{64} \).

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

Simplify the expression \( \frac{(2a^3)^4}{8a^5} \) and leave your answer in index form.

Write your answer out first, then check it against the worked solution.

Question 8

2 marks

Express the number 1,000,000 as a power of 10.

Write your answer out first, then check it against the worked solution.

Question 9

4 marks

Find the value of \( \sqrt{144} - \sqrt[3]{64} + 2^5 \).

Write your answer out first, then check it against the worked solution.

Question 10

4 marks

Evaluate the following expression and give your answer in index form:
\( \frac{5^8 \times 5^3}{(5^2)^4} \)

Write your answer out first, then check it against the worked solution.

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