4024/11 May/Jun 2022, Question 15: Laws of Indices
Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Work with index laws: evaluate a quotient of powers of 7, find k in a power equation, and simplify a squared product into prime-power form.
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Part (a) · 1 mark
Evaluate 7⁻³ ÷ 7⁻⁴.
- 17⁻³ ÷ 7⁻⁴ = 7⁻³⁺⁴ = 7¹ = 7
Answer7
Part (b) · 1 mark
Find k such that (3⁶)ᵏ = 3².
- 13⁶ᵏ = 3² → 6k = 2
- 2k = 1/3
Answer1/3
Part (c) · 2 marks
Simplify 3(2² × 3³ × 5⁴)² and give it as 2ᵃ × 3ᵇ × 5ᶜ.
- 1(2² × 3³ × 5⁴)² = 2⁴ × 3⁶ × 5⁸
- 23 × 2⁴ × 3⁶ × 5⁸ = 2⁴ × 3⁷ × 5⁸
Answer2⁴ × 3⁷ × 5⁸
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Also searched as: 4024/11/M/J/22 · 4024_s22_qp_11 · 4024 s22 11 · question 15.
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