Question

Choose the right answer from the options given after every question.

${\left[{\left(\frac{3}{7}\right)}^{-3}\right]}^4$ = ................

(i) ${\left(\frac{3}{7}\right)}^{-7}$ (ii) ${\left(\frac{3}{7}\right)}^{-10}$ (iii) ${\left(\frac{7}{3}\right)}^{12}$ (iv) ${\left(\frac{3}{7}\right)}^{20}$

Answer 1

$$\begin{gathered} {\left[{\left(\frac{3}{7}\right)}^{-3}\right]}^4={\left(\frac{3}{7}\right)}^{-3\left(4\right)}\left[\because {\left(a^m\right)}^n=a^{mn}\right] \\ ={\left(\frac{3}{7}\right)}^{-12} \\ ={\left(\frac{7}{3}\right)}^{12}\left[\because {\left(a\right)}^{-n}=\frac{1}{a^n}\right] \end{gathered}$$
​Hence, the correct option is (iii).