4MA1/2HR Jun 2025, Question 6: Laws of Indices
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
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The question, in short
Evaluate a zero power, find an unknown index k from a quotient of powers of 5, and simplify a cubed product of algebraic terms.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 1 mark
State the value of 5 to the power 0.
- 1Any non-zero number to the power 0 is 1
- 25⁰ = 1
Answer1
Part (b) · 2 marks
Given (5⁹ × 5⁻³) ÷ 5⁻² = 5ᵏ, find the value of k.
- 15⁹ × 5⁻³ = 5⁹⁻³ = 5⁶
- 25⁶ ÷ 5⁻² = 5⁶⁺² = 5⁸
- 3k = 8
Answer8
Part (c) · 2 marks
Simplify fully (2d⁴e⁵)³.
- 12³ = 8
- 2(d⁴)³ = d¹²
- 3(e⁵)³ = e¹⁵
- 4(2d⁴e⁵)³ = 8d¹²e¹⁵
Answer8d¹²e¹⁵
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