Cambridge IGCSE · Mathematics (0580)

Indices I: Practice Questions

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

10 questions25 marksFree, no account

Question 1

1 mark

Calculate the value of \( 7^0 \times 2^3 \).

Question 2

1 mark

Simplify the following expression using the rules of indices:
\( \frac{(y^3)^2}{y^{-2} \times y^5} \)

Question 3

1 mark

Simplify the expression \( \frac{(2a^3b^{-2})^3}{4a^5b^2} \).

Question 4

1 mark

Evaluate \( 5^3 \times 5^0 \div 5^1 \).

Question 5

1 mark

Simplify the expression \( \frac{x^8}{x^{-2}} \).

Question 6

2 marks

Simplify the expression \( \frac{x^7 \times x^{-3}}{x^2} \).

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

Question 7

4 marks

Evaluate \( \left(\frac{1}{49}\right)^{-\frac{1}{2}} \).

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

Question 8

5 marks

Evaluate \( \frac{25^{3/2}}{100^{1/2}} \).

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

Question 9

4 marks

(a) Evaluate the following, showing your working:

(i) \( 7^0 \)
(ii) \( 2^{-3} \)

(b) Simplify the expression \( \frac{x^4 \times x^6}{x^2} \), giving your answer in index form.

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

Question 10

5 marks

Solve the equation \( 8^{2x-1} = 4^x \).

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

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