iGCSE Mathematics (0580) - C2.4 Indices II- Exam Style Questions Paper 1- New Syllabus
▶️ Answer/Explanation
(a)
When multiplying powers of the same base, add the indices: \(a^8 \times a^x = a^{8+x}\).
Setting the exponent equal to 15: \(8 + x = 15\), so \(x = 7\).
✅ Answer: \(x = 7\)
(b)
When raising a power to a power, multiply the indices: \((b^7)^y = b^{7y}\).
Setting the exponent equal to 21: \(7y = 21\), so \(y = 3\).
✅ Answer: \(y = 3\)
▶️ Answer/Explanation
(a) When multiplying terms with the same base, we keep the base and add the exponents: $y^{4+6} = y^{10}$.
(b) When dividing terms with identical bases, we subtract the exponent of the denominator from the numerator: $p^{5-8} = p^{-3}$, which can also be neatly expressed as $\frac{1}{p^3}$.
(c) For a power raised to another power, we multiply the indices together: $w^{4 \times 3} = w^{12}$.
Answers:
(a) $y^{10}$
(b) $\frac{1}{p^{3}}$ or $p^{-3}$
(c) $w^{12}$