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Question

# Find the values of the following: (1) 113 (2) (–5)2 (3) (–3)3 (4) 107 (5) 24 (6) ${\left(\frac{2}{3}\right)}^{5}$ (7) ${\left(-\frac{1}{5}\right)}^{4}$ (8) 28 (9) (–1)8 (10) (–1)9

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Solution

## (1) (11)3 = 11 × 11 × 11 = 1331 (2) (–5)2 = (–5) × (–5) (Product of negative sign is positive if multiplied for an even number of times) = 25 (3) (–3)3 = (–3) × (–3) × (–3) (Product of negative sign is negative if multiplied for an odd number of times) = –27 (4) 107 = 10 × 10 × 10 × 10 × 10 × 10 × 10 = 10000000 (5) 24 = 2 × 2 × 2 × 2 = 16 (6) ${\left(\frac{2}{3}\right)}^{5}$ $=\left(\frac{2}{3}\right)×\left(\frac{2}{3}\right)×\left(\frac{2}{3}\right)×\left(\frac{2}{3}\right)×\left(\frac{2}{3}\right)\phantom{\rule{0ex}{0ex}}=\frac{32}{243}$ (7) ${\left(-\frac{1}{5}\right)}^{4}$ $=\left(-\frac{1}{5}\right)×\left(-\frac{1}{5}\right)×\left(-\frac{1}{5}\right)×\left(-\frac{1}{5}\right)$ (Product of negative sign is positive if multiplied for an even number of times) $=\frac{1}{625}$ (8) 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256 (9) (–1)8 = (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) (Product of negative sign is positive if multiplied for an even number of times) = 1 (10) (–1)9 = (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) (Product of negative sign is negative if multiplied for an odd number of times) = –1

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