0580/12 Feb/Mar 2021, Question 18: Index Laws with Letters
Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 3 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Simplify two index expressions and solve an equation with 3 to the power p equal to 1/81 to find p.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (ai) · 1 mark
Simplify x¹² ÷ x³, giving the result as a single power of x.
- 1x¹² ÷ x³ = x¹²⁻³ = x⁹
Answerx⁹
Part (aii) · 1 mark
Simplify (y²)⁵, writing the answer as a single power of y.
- 1(y²)⁵ = y^(2 × 5) = y¹⁰
Answery¹⁰
Part (b) · 1 mark
Given 3ᵖ = 1/81, find the value of p.
- 181 = 3⁴ so 1/81 = 3⁻⁴
- 2p = −4
Answer−4
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