0580/23 Oct/Nov 2024, Question 17: Index Laws with Letters

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 4 marks

The question, in short

Simplify two algebraic expressions: a quotient of powers of x with coefficients, and a power of a coefficient times y raised to a fractional exponent.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Simplify 18x¹⁸ ÷ 3x³, giving the result as a single term.

118 ÷ 3 = 6 and x¹⁸ ÷ x³ = x¹⁸⁻³ = x¹⁵
2= 6x¹⁵

Answer6x¹⁵

Part (b) · 2 marks

Simplify (125y⁷⁵)^(2/3), evaluating the numerical coefficient and the exponent of y.

1125^(2/3) = (∛125)² = 5² = 25
2(y⁷⁵)^(2/3) = y^(75 × 2/3) = y⁵⁰
3= 25y⁵⁰

Answer25y⁵⁰

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0580/23 Oct/Nov 2024, Question 17: Index Laws with Letters

The question, in short

Part (a) · 2 marks

Part (b) · 2 marks

Practise more index laws with letters questions

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