4MA1/1F Jun 2025, Question 21: Index Laws with Letters
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 4 marks
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The question, in short
Apply index laws to find m in x⁵ × x⁷ = xᵐ, find n in y⁸ ÷ y³ = yⁿ, and simplify (5a⁴r²)³ fully.
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Part (a) · 1 mark
Find the value of m from x⁵ × x⁷ = xᵐ.
- 1x⁵ × x⁷ = x⁵⁺⁷
- 2= x¹²
- 3m = 12
Answer12
Part (b) · 1 mark
Find the value of n from y⁸ ÷ y³ = yⁿ.
- 1y⁸ ÷ y³ = y⁸⁻³
- 2= y⁵
- 3n = 5
Answer5
Part (c) · 2 marks
Simplify fully the expression (5a⁴r²)³.
- 15³ = 125
- 2(a⁴)³ = a¹²
- 3(r²)³ = r⁶
- 4125a¹²r⁶
Answer125a¹²r⁶
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