Tick (✓) the correct answer

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) $\frac{-8}{9}$

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

$\sqrt[3]{\frac{-512}{729}}=\frac{-8}{9}$

$\therefore \sqrt[3]{\frac{-512}{729}}=\frac{-8}{9}$

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