Question

[3√x^4yX 1/3√xy^7]^-4
Simplify​

Answer 1

$\: \: \: \: \sqrt[3]{ {x}^{4}y } \times \frac{1}{ \sqrt[3]{x {y}^{7} } } \\ = \frac{ \sqrt[3]{ {x}^{4}y } }{ \sqrt[3]{x {y}^{7} } } \\ = \sqrt[3]{ \frac{ {x}^{4} y}{x {y}^{7} } } \\ = \sqrt[3]{ \frac{ {x}^{3} }{ {y}^{6} }} = {( \frac{ {x}^{3} }{ {y}^{6} }) }^{ \frac{1}{3} } \\ = \frac{ {( {x}^{3} )}^{ \frac{1}{3} } }{ {( {y}^{6}) }^{ \frac{1}{3} } } = \frac{ {x}^{3 \times \frac{1}{3} } }{ {y}^{6 \times \frac{1}{3} } } = \frac{ {x}^{1} }{ {y}^{2} } \\ = \frac{x}{ {y}^{2} }$