Question

$\tt{Determine\: \:the\: \: cube\:\: root \: \: of\: -512a^2b^3}$

Answer 1

The cube root of 512 is the number which when multiplied by itself three times gives the product as 512. Since 512 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Therefore, the cube root of 512 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 8.

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Answer 2

Answer:

${-8ba^\frac{2}{3} }$

Step-by-step explanation:

We have:

$\Rightarrow \sqrt[3]{-512a^2b^3}$

$\Rightarrow \sqrt[3]{-2^9\times a^2b^3}$

$\rightarrow {(-2)^{9 \times \frac{1}{3}}} \times a^{2\times \frac{1}{3}} \times b^{3\times \frac{1}{3}}$

$\Rightarrow {-8ba^\frac{2}{3} }$ is the cube root.