Cambridge IGCSE · International Mathematics (0607)

Indices I: Practice Questions

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

10 questions28 marksFree, no account

Question 1

1 mark

Evaluate the expression:
\( 5^3 \times 2^3 \div 10^2 \)

Question 2

1 mark

Find the value of \( a \) that satisfies the equation:
\( 2^a = \sqrt{32} \times 2^{-3} \)

Question 3

1 mark

Find the value of the following numerical expression:
\( 16^{-\frac{1}{2}} \times 8^{\frac{2}{3}} \)

Question 4

1 mark

Determine the value of \(x\) that satisfies the following equation:
\(10^x = 0.001 \times 10^5\)

Question 5

1 mark

Find the value of \((3^2)^{-3} \times 3^4\) as a fraction in its simplest form.

Question 6

3 marks

Find the value of the following expression:
\( (0.25)^{-2} \)

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

Question 7

6 marks

Simplify the following expression and write your answer with positive indices:
\( \frac{(25x^4)^{-\frac{1}{2}}}{x^{-5}} \)

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

Question 8

3 marks

Solve for \( x \) in the following equation:
\( 5^x = \frac{1}{125} \)

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

Question 9

5 marks

Solve the following equations for \( x \):
(a) \( 2^x = 64 \)
(b) \( 5^{x-1} = \frac{1}{25} \)
(c) \( 10^x = 0.001 \)

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

Question 10

6 marks

Solve the equation:
\( \left( \frac{1}{4} \right)^{2x-3} = 8^{x+1} \)

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

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