4024/12 Oct/Nov 2025, Question 19: Fractional Indices
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Evaluate 16^(−3/4) and express 9² × 3^(−1/2) as a single power of 3.
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Part (a) · 2 marks
Find the value of 16 raised to the power −3/4.
- 116^(1/4) = 2, so 16^(3/4) = 2³ = 8
- 216^(−3/4) = 1/8
Answer1/8
Part (b) · 2 marks
Rewrite 9² × 3^(−1/2) as one power of 3.
- 19² = (3²)² = 3⁴
- 23⁴ × 3^(−1/2) = 3^(4 − 1/2)
- 3= 3^(7/2)
Answer3^(7/2)
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Also searched as: 4024/12/O/N/25 · 4024_w25_qp_12 · 4024 w25 12 · question 19.
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