Simplify each of the following:

Solution:

(i) $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}$

(Note: $\sqrt[n]{a} \times \sqrt[n]{b}=\sqrt[n]{a \times b}$ )

$=\sqrt[3]{4 \times 16}$

$=\sqrt[3]{64}$

$=\sqrt[3]{4^{3}}$

$=\left(4^{3}\right)^{1 / 3}$

$=4^{(3 \times 1 / 3)}$

$=4^{1}$

$=4$

(ii) $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}$

$\left(\right.$ Note: $\left.\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}\right)$

$=\sqrt[4]{\frac{1250}{2}}$

$=\sqrt[4]{\frac{2 \times 625}{2}}$

$=\sqrt[4]{625}$

$=\sqrt[4]{15^{4}}$

$=15^{(4 \times 1 / 4)}$

$=15$