Question

Tick (✓) the correct answer
$\sqrt[3]{\frac{-512}{729}}=?$
(a) $\frac{-7}{9}$
(b) $\frac{-8}{9}$
(c) $\frac{7}{9}$
(d) $\frac{8}{9}$

Answer 1

(b) $\frac{-8}{9}$
$\sqrt[3]{\frac{-512}{729}}$= $\frac{\sqrt[3]{-512}}{\sqrt[3]{729}}=\frac{\sqrt[3]{\left(-8\right)\times \left(-8\right)\times \left(-8\right)}}{\sqrt[3]{9\times 9\times 9}}=\frac{\sqrt[3]{{\left(-8\right)}^3}}{\sqrt[3]{{\left(9\right)}^3}}$
$\sqrt[3]{\frac{-512}{729}}$ = $\frac{-8}{9}$
∴ $\sqrt[3]{\frac{-512}{729}}$ = $\frac{-8}{9}$