Question

Evaluate :
(i) $\sqrt[3]{3\frac{-125}{343}}$

(ii) $\sqrt[3]{3\frac{216}{729}}$

Answer 1

(1) $\sqrt[3]{3\frac{-125}{343}}$

using ${\left(\frac{a}{b}\right)}^n=\frac{a^n}{b^n}$

$\Rightarrow \frac{\sqrt[3]{3-125}}{\sqrt[3]{3343}}=\frac{-5}{7}$

$\left(i1\right)\sqrt[3]{3\frac{216}{729}}=\frac{\sqrt[3]{3216}}{3\sqrt{729}}=\frac{6}{9}=\frac{2}{3}$