Solve the following

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:

$\left(\left(\frac{1}{3}\right)^{2}\right)^{4}=\left(\frac{1}{3}\right)^{2 \times 4} \quad \ldots\left(\left(a^{m}\right)^{n}=a^{m \times n}\right)$

$=\left(\frac{1}{3}\right)^{8}$

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