Question:
Tick (✓) the correct answer
$\sqrt[3]{\frac{-512}{729}}=?$
(a) $\frac{-7}{9}$
(b) $\frac{-8}{9}$
(C) $\frac{7}{9}$
(d) $\frac{8}{9}$
Solution:
(b) $\frac{-8}{9}$
$\sqrt[3]{\frac{-512}{729}}=\frac{\sqrt[3]{-512}}{\sqrt[3]{729}}=\frac{\sqrt[3]{(-8) \times(-8) \times(-8)}}{\sqrt[3]{9 \times 9 \times 9}}=\frac{\sqrt[3]{(-8)^{3}}}{\sqrt[3]{(9)^{3}}}$
$\sqrt[3]{\frac{-512}{729}}=\frac{-8}{9}$
$\therefore \sqrt[3]{\frac{-512}{729}}=\frac{-8}{9}$