4MA1/2F Nov 2021, Question 17: Laws of Indices
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 4 marks
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The question, in short
Using index laws, determine the unknown exponents m, n and p in three equations involving powers of 3, 5 and 7.
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Part (a) · 1 mark
Find m so that 3⁴ × 3⁵ equals 3ᵐ.
- 1When multiplying, add the powers: 3⁴ × 3⁵ = 3⁴⁺⁵ = 3⁹
- 2m = 9
Answer9
Part (b) · 1 mark
Find n so that (5³)⁷ equals 5ⁿ.
- 1Power of a power: multiply the powers, 3 × 7 = 21
- 2(5³)⁷ = 5²¹, so n = 21
Answer21
Part (c) · 2 marks
Find p so that (7⁸ × 7²) ÷ 7ᵖ equals 7⁶.
- 17⁸ × 7² = 7¹⁰
- 27¹⁰ ÷ 7ᵖ = 7¹⁰⁻ᵖ = 7⁶
- 310 − p = 6, so p = 4
Answer4
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