4024/12 Oct/Nov 2021, Question 22: Exponential Equations
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Solve an exponential equation with base 27 equal to 9, then simplify an expression with a negative fractional power involving 16 and x⁸.
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Part (a) · 2 marks
Find the value of k that satisfies 27ᵏ = 9.
- 127 = 3³ and 9 = 3²
- 23³ᵏ = 3² → 3k = 2
- 3k = 2/3
Answer2/3
Part (b) · 2 marks
Simplify (16/x⁸)^(−1/4), giving the result in simplified form.
- 1A negative power flips the fraction: (16/x⁸)^(−1/4) = (x⁸/16)^(1/4)
- 2Power 1/4 means fourth root: ⁴√(x⁸) = x² and ⁴√16 = 2
- 3So the answer is x²/2
Answerx²/2
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Also searched as: 4024/12/O/N/21 · 4024_w21_qp_12 · 4024 w21 12 · question 22.
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