4MA1/2FR Jun 2025, Question 22: Laws of Indices
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 5 marks
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The question, in short
Evaluate a zero index, find the exponent k in a quotient of powers of 5, and cube the expression (2d⁴e⁵)³.
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Part (a) · 1 mark
State the value of 5⁰.
- 1Any non-zero number to the power 0 is 1
- 25⁰ = 1
Answer1
Part (b) · 2 marks
Find k so that (5⁹ × 5⁻³)/5⁻² equals 5ᵏ.
- 15⁹ × 5⁻³ = 5⁹⁻³ = 5⁶
- 25⁶ ÷ 5⁻² = 5⁶⁻⁽⁻²⁾ = 5⁸
- 3k = 8
Answer8
Part (c) · 2 marks
Simplify (2d⁴e⁵)³ fully.
- 12³ = 8
- 2(d⁴)³ = d¹²
- 3(e⁵)³ = e¹⁵
- 4(2d⁴e⁵)³ = 8d¹²e¹⁵
Answer8d¹²e¹⁵
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