4024/13 May/Jun 2026, Question 21: Exponential Equations
Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 5 marks
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The question, in short
Simplify a power expression with a negative fractional index, then solve an exponential equation for x.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Simplify (25 ÷ x⁴) raised to the power −3/2, giving the result in simplest form.
- 1(25/x⁴)^(−3/2) = (x⁴/25)^(3/2)
- 2√(x⁴/25) = x²/5
- 3(x²/5)³ = x⁶/125
Answerx⁶/125
Part (b) · 3 marks
Find the value of x satisfying 8ˣ = 4ˣ⁺³.
- 18ˣ = 2³ˣ and 4ˣ⁺³ = 2²⁽ˣ⁺³⁾ = 2²ˣ⁺⁶
- 23x = 2x + 6
- 3x = 6
Answer6
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Also searched as: 4024/13/M/J/26 · 4024_s26_qp_13 · 4024 s26 13 · question 21.
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