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Question

Write each of the following in power notation: (i) $\frac{5}{7}×\frac{5}{7}×\frac{5}{7}×\frac{5}{7}$ (ii) $\left(\frac{-4}{3}\right)×\left(\frac{-4}{3}\right)×\left(\frac{-4}{3}\right)×\left(\frac{-4}{3}\right)×\left(\frac{-4}{3}\right)$ (iii) $\left(\frac{-1}{6}\right)×\left(\frac{-1}{6}\right)×\left(\frac{-1}{6}\right)$ (iv) (−8) × (−8) × (−8) × (−8) × (−8)

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Solution

(i) $\frac{5}{7}×\frac{5}{7}×\frac{5}{7}×\frac{5}{7}={\left(\frac{5}{7}\right)}^{4}$ (ii) $\left(\frac{-4}{3}\right)×\left(\frac{-4}{3}\right)×\left(\frac{-4}{3}\right)×\left(\frac{-4}{3}\right)×\left(\frac{-4}{3}\right)={\left(\frac{-4}{3}\right)}^{5}$ (iii) $\left(\frac{-1}{6}\right)×\left(\frac{-1}{6}\right)×\left(\frac{-1}{6}\right)={\left(\frac{-1}{6}\right)}^{3}$ (iv) $\left(-8\right)×\left(-8\right)×\left(-8\right)×\left(-8\right)×\left(-8\right)={\left(-8\right)}^{5}$

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