Question:
Mark (✓) against the correct answer
$\frac{\sqrt[3]{128}}{\sqrt[3]{250}}=?$
(a) $\frac{3}{5}$
(b) $\frac{4}{5}$
(C) $\frac{2}{5}$
(d) none of these
Solution:
(b) $\frac{4}{5}$
Resolving the numerator and the denominator into prime factors:
$\frac{\sqrt[3]{128}}{\sqrt[3]{250}}=\sqrt[3]{\frac{128}{250}}=\sqrt[3]{\frac{2 \times 8 \times 8}{2 \times 5 \times 5 \times 5}}=\sqrt[3]{\frac{\not 2 \times 8 \times 8}{\not 2 \times 5 \times 5 \times 5}}=\sqrt[3]{\frac{8 \times 8}{5 \times 5 \times 5}}$
$=\sqrt[3]{\frac{(2)^{3} \times(2)^{3}}{(5)^{3}}}=\frac{2 \times 2}{5}=\frac{4}{5}$