Find: <br/><br/>(i)$64^{\frac{1}{2}}$ <br/><br/> (ii) $32^{\frac{1}{5}}$ <br/><br/>(iii)$125^{\frac{1}{3}}$

Solution:

(i) $64^{\frac{1}{2}}=\left(2^{6}\right)^{\frac{1}{2}}$

$=2^{6 x \frac{1}{2}}$

$\left[\left(a^{m}\right)^{n}=a^{m n}\right]$

$=2^{3}=8$ (ii) $32^{\frac{1}{5}}=\left(2^{5}\right)^{\frac{1}{5}}$

$=(2)^{5 \times \frac{1}{5}}$

$\left[\left(a^{m}\right)^{n}=a^{m n n}\right]$

$=2^{1}=2$ (iii) $(125)^{\frac{1}{3}}=\left(5^{3}\right)^{\frac{1}{3}}$

$=5^{3 \times \frac{1}{3}}$

$\left[\left(a^{m}\right)^{n}=a^{m n}\right]$

$=5^{1}=5$