Evaluate
(i) $\left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}}$
(ii) $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}$
(iii) $\frac{2^{0}+7^{0}}{5^{0}}$
(iv) $\left[(16)^{\frac{1}{2}}\right]^{\frac{1}{2}}$
(i) $\left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}}$
$\left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}}=(1+8+27)^{\frac{1}{2}}$
$=(36)^{\frac{1}{2}}$
$=\left[(6)^{2}\right]^{\frac{1}{2}}$
$=6$
(ii) $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}$
$\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}=\left\{5\left[\left[(2)^{3}\right]^{\frac{1}{3}}+\left[(3)^{3}\right]^{\frac{1}{3}}\right]^{3}\right\}^{\frac{1}{4}}$
$=\left[5(2+3)^{3}\right]^{\frac{1}{4}}$
$=\left[(5)^{4}\right]^{\frac{1}{4}}$
$=5$
(iii) $\frac{2^{0}+7^{0}}{5^{0}}$
$\frac{2^{0}+7^{0}}{5^{0}}=\frac{1+1}{1}$
$=2$
(iv) $\left[(16)^{\frac{1}{2}}\right]^{\frac{1}{2}}$
$\left[(16)^{\frac{1}{2}}\right]^{\frac{1}{2}}=\left\{\left[(4)^{2}\right]^{\frac{1}{2}}\right\}^{\frac{1}{2}}$
$=\left[(4)^{1}\right]^{\frac{1}{2}}$
$=\left[(2)^{2}\right]^{\frac{1}{2}}$
$=2$
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