Question

simplify and Express the answer with positive exponent

Answer 1

$\textbf{Given:}$

$[\sqrt[3]{x^4y}{\times}\dfrac{1}{\sqrt[3]{xy^7}}]^{-4}$

$\textbf{To find:}$

$\text{Simplified form of}\;\;[\sqrt[3]{x^4}{\times}\dfrac{1}{\sqrt[3]{xy^7}}]^{-4}$

$\textbf{Solution:}$

$\text{Consider,}$

$[\sqrt[3]{x^4y}{\times}\dfrac{1}{\sqrt[3]{xy^7}}]^{-4}$

$=[\dfrac{\sqrt[3]{x^4y}}{\sqrt[3]{xy^7}}]^{-4}$

$=[\sqrt[3]{\dfrac{x^4y}{xy^7}}]^{-4}$

$=[\sqrt[3]{\dfrac{x^3}{y^6}}]^{-4}$

$=[\sqrt[3]{(\dfrac{x}{y^2})^3}]^{-4}$

$=[\dfrac{x}{y^2}]^{-4}$

$=\dfrac{x^{-4}}{y^{-8}}$

$=\dfrac{\dfrac{1}{x^4}}{\dfrac{1}{y^8}}$

$=\dfrac{1}{x^4}{\times}\dfrac{y^8}{1}$

$=\dfrac{y^8}{x^4}$

$\textbf{Answer:}$

$\boxed{\bf\,[\sqrt[3]{x^4y}{\times}\dfrac{1}{\sqrt[3]{xy^7}}]^{-4}=\dfrac{y^8}{x^4}}$

Answer 2

For answer refer to the attachment

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