Question:
$\left\{\left(\frac{1}{3}\right)^{2}\right\}^{4}$ is equal to
(a) $\left(\frac{1}{3}\right)^{6}$
(b) $\left(\frac{1}{3}\right)^{8}$
(c) $\left(\frac{1}{3}\right)^{24}$
(d) $\left(\frac{1}{3}\right)^{16}$
Solution:
(b) (1/3)8
We have:
$\left(\left(\frac{1}{3}\right)^{2}\right)^{4}=\left(\frac{1}{3}\right)^{2 \times 4} \quad \ldots\left(\left(a^{m}\right)^{n}=a^{m \times n}\right)$
$=\left(\frac{1}{3}\right)^{8}$