Question

$\huge{\underline{\mathtt{\red{Q}\pink{U}\green{E}\blue{S}\purple{T}\orange{I}\red{0}\pink{N}}}}$
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Answer 1

⠀⠀⌬⠀ Evaluate :

$\begin{gathered}\qquad \qquad \bigstar \sf \Bigg\{ \sqrt[3]{x^4 y} \:\times \:\dfrac{1}{\sqrt[4]{x^2y^8}}\:\Bigg\}\:^{-6}\:\times \: \dfrac{x}{y}\:\\\\\end{gathered}$

$\begin{gathered}\qquad \bigstar \:\:\underline {\purple {\pmb{\sf By \: \:Using \:the \:Given \:\::\:}}}\\\\\end{gathered}$

$\begin{gathered}\qquad \twoheadrightarrow \sf \Bigg\{ \sqrt[3]{x^4 y} \:\times \:\dfrac{1}{\sqrt[4]{x^2y^8}}\:\Bigg\}\:^{-6}\:\times \: \dfrac{x}{y}\:\\\\\end{gathered}$

$\begin{gathered}\qquad \twoheadrightarrow \sf \Bigg\{ \big( x^4 y\big)^{\frac{1}{3}} \:\times \:\dfrac{1}{\big( x^2y^8\big)^{\frac{1}{4}}\:}\Bigg\}\:^{-6}\:\times \: \dfrac{x}{y}\:\\\\\end{gathered}$

$\begin{gathered}\qquad \twoheadrightarrow \sf \Bigg\{ x^{\frac{4}{3} } y^{\frac{1}{3}} \:\times \:\dfrac{1}{\big( x^2y^8\big)^{\frac{1}{4}}}\:\Bigg\}\:^{-6}\:\times \: \dfrac{x}{y}\:\\\\\end{gathered}$

$\begin{gathered}\qquad \twoheadrightarrow \sf \Bigg\{ x^{\frac{4}{3} } y^{\frac{1}{3}} \:\times \:\dfrac{1}{ x^{\frac{2}{4}}y^{\frac{8}{4}}}\:\Bigg\}\:^{-6}\:\times \: \dfrac{x}{y}\:\\\\\end{gathered}$

$\begin{gathered}\qquad \twoheadrightarrow \sf \Bigg\{ x^{\frac{4}{3} } y^{\frac{1}{3}} \:\times \:\dfrac{1}{ x^{\frac{1}{2}}y^{2}}\:\Bigg\}\:^{-6}\:\times \: \dfrac{x}{y}\:\\\\\end{gathered}$

$\begin{gathered}\qquad \twoheadrightarrow \sf \Bigg\{ x^{\bigg[ \frac{4}{3} - \frac{1}{2} \big] } \:\times\:y^{\bigg[ \frac{1}{3} - 2 \bigg] } \:\:\Bigg\}\:^{-6}\:\times \: \dfrac{x}{y}\:\\\\\\\qquad \twoheadrightarrow \sf \Bigg\{ x^{\bigg[ \frac{8 - 3 }{6} \bigg] } \:\times\:y^{\bigg[ \frac{1 - 6 }{3} \bigg] } \:\:\Bigg\}\:^{-6}\:\times \: \dfrac{x}{y}\:\\\\\\\qquad \twoheadrightarrow \sf \Bigg\{ x^{\bigg[ \frac{5 }{ 6} \bigg] } \:\times\:y^{\bigg[ \frac{ -5 }{3} \bigg] } \:\:\Bigg\}\:^{-6}\:\times \: \dfrac{x}{y}\:\\\\\\\qquad \twoheadrightarrow \sf \Bigg\{ x^{\bigg[ \frac{5 }{6} \:\times \big( - 6 \big) \bigg] } \:\times\:y^{\bigg[ \frac{ -5 }{3} \:\times \big( - 6 \big) \bigg] } \:\:\Bigg\}\:\:\times \: \dfrac{x}{y}\:\\\\\\\qquad \twoheadrightarrow \sf \Bigg\{ x^{ -5 } \:\times\:y^{ 10 \: } \:\:\Bigg\}\:\:\times \: \dfrac{x}{y}\:\\\\\\\qquad \twoheadrightarrow \sf \Bigg\{ x^{ \big[ -5 + 1 \big] } \:\times\:y^{ \big[10 - 1 \big] \: } \:\:\Bigg\}\:\:\:\\\\\\\qquad \twoheadrightarrow \pmb{\purple { \sf \big\{ x^{ -4 } \:\times\:y^{ 9 \: } \:\:\big\}\:}}\:\:\bigstar \:\:\\\\\end{gathered}$