Simplify:
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 $)\left(\frac{1}{3^{4}}\right)^{\frac{1}{2}}=\left(\frac{1}{3}\right)^{4 \times \frac{1}{2}}=\left(\frac{1}{3}\right)^{2}=\frac{1}{9}=3^{-2}$

 

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