Question

Simplify:
(i) (3⁴)^1/4
(ii) (3^1/3)⁴
(iii) $\left(\frac{1}{3^4}\right)$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right){\left(3^4\right)}^{\frac{1}{4}}=3^{4\times \frac{1}{4}}=3\left[{\left((a{)}^m\right)}^n=a^{mn}\right] \\ \left(\mathrm{ii}\right){\left(3^{\frac{1}{3}}\right)}^4=3^{\frac{1}{3}\times 4}=3^{\frac{4}{3}} \\ \left(\mathrm{iii}\right){\left({\displaystyle \frac{1}{3^4}}\right)}^{\frac{1}{2}}={\left(\frac{1}{3}\right)}^{4\times \frac{1}{2}}={\left(\frac{1}{3}\right)}^2=\frac{1}{9}=3^{-2} \end{gathered}$$