Cambridge IGCSE · Mathematics (0580)

Powers and roots: Practice Questions

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

10 questions25 marksFree, no account

Question 1

1 mark

Calculate the value of $ \sqrt{144} + 4^3 $.

Question 2

1 mark

Evaluate $ 81^{\frac{3}{4}} $.

Question 3

1 mark

If $ p^{-\frac{1}{2}} = \frac{1}{4} $, find the value of $ p $.

Question 4

1 mark

Calculate the value of $ (3^2 - \sqrt{25}) \div 2 $.

Question 5

1 mark

Calculate the exact value of the following expression:
$ \sqrt[3]{216} \times 4^{-\frac{3}{2}} + \sqrt{0.25} $

Question 6

2 marks

Calculate the value of $$ \sqrt[3]{125} + 4^2 $$.

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

Question 7

3 marks

Evaluate $ (64^{1/3})^2 $.

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

Question 8

5 marks

If $ 4^m = 8^{m-1} $, find the value of $ m $.

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Question 9

5 marks

Work out the value of each of the following:

(a) $8^2$

(b) $\sqrt{121}$

(c) $3^3$

(d) $\sqrt[3]{64}$

(e) $2^4 \times 5^0$

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

Question 10

5 marks

Simplify the following expressions, giving your answers with positive indices only:

(a) $$ (3x^2y^{-3})^2 \times 2x^{-1}y^5 $$

(b) $$ \frac{10a^5b^2}{(5a^{-2}b^4)^{-1}} $$

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

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