iGCSE Mathematics (0580) :E1.7 Understand the meaning of indices (fractional, negative and zero) and use the rules of indices. iGCSE Style Questions Paper 2

Question

(a) $3^{3p} \times 3^{2p} = 729$

Find the value of p.

(b) Simplify $(32x^{10})^{\frac{1}{5}}$

▶️ Answer/Explanation

Solution

(a) Ans: 1.2

$3^{5p} = 3^6$ (since $729 = 3^6$)

$5p = 6 \Rightarrow p = \frac{6}{5} = 1.2$

(b) Ans: $2x^2$

$(32)^{\frac{1}{5}} = 2$ and $(x^{10})^{\frac{1}{5}} = x^2$

Final answer: $2x^2$

Question

Simplify.

(a) $ n^5 \times n $

(b) $ 8x^6 \div 2x^2 $

▶️ Answer/Explanation

Solution

(a) Ans: $ n^6 $

When multiplying with same base, add exponents: $ n^5 \times n^1 = n^{5+1} = n^6 $

(b) Ans: $ 4x^4 $

Divide coefficients and subtract exponents: $ (8÷2)x^{6-2} = 4x^4 $

(c) Ans: $ 9y^8 $

1. Recognize 243 as 3⁵: $ (3^5 y^{20})^{2/5} $

2. Apply exponent to both parts: $ 3^{5×(2/5)} × y^{20×(2/5)} $

3. Simplify: $ 3^2 × y^8 = 9y^8 $

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