Question:
Simplify:
(i) $\left(3^{4}\right)^{1 / 4}$
(ii) $\left(3^{1 / 3}\right)^{4}$
(iii) $\left(\frac{1}{3^{4}}\right)$
Solution:
$(\mathrm{i})\left(3^{4}\right)^{\frac{1}{4}}=3^{4 \times \frac{1}{4}}=3$
$\left[\left((a)^{m}\right)^{n}=a^{m n}\right]$
$(\mathrm{ii})\left(3^{\frac{1}{3}}\right)^{4}=3^{\frac{1}{3} \times 4}=3^{\frac{4}{3}}$
$($ iii $)\left(\frac{1}{3^{4}}\right)^{\frac{1}{2}}=\left(\frac{1}{3}\right)^{4 \times \frac{1}{2}}=\left(\frac{1}{3}\right)^{2}=\frac{1}{9}=3^{-2}$