Question:
$\left(\frac{2}{3}\right)^{-5} \times\left(\frac{5}{7}\right)^{-5}$ is equal to
(a) $\left(\frac{2}{3} \times \frac{5}{7}\right)^{-10}$
(b) $\left(\frac{2}{3} \times \frac{5}{7}\right)^{-5}$
(c) $\left(\frac{2}{3} \times \frac{5}{7}\right)^{25}$
(d) $\left(\frac{2}{3} \times \frac{5}{7}\right)^{-25}$
Solution:
(b) $\left(\frac{2}{3} \times \frac{5}{7}\right)^{-5}$
We have:
$\left(\frac{2}{3}\right)^{-5} \times\left(\frac{5}{7}\right)^{-5}=\left(\frac{2}{3} \times \frac{5}{7}\right)^{-5} \quad \cdots\left((a \times b)^{n}=a^{n} \times b^{n}\right)$
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