The value of(32243)−45 is = ?The value of(32243)−45 is = ?\eqalign{ & {\text{The value of}} \cr & {\left( {\frac{{32}}{{243}}} \right)^{ - \frac{4}{5}}}{\text{ is = ?}} \cr} " /> The value of(32243)−45 is = ?The value of(32243)−45 is = ?\eqalign{ & {\text{The value of}} \cr & {\left( {\frac{{32}}{{243}}} \right)^{ - \frac{4}{5}}}{\text{ is = ?}} \cr} " /> The value of(32243)−45 is = ?The value of(32243)−45 is = ?\eqalign{ & {\text{The value of}} \cr & {\left( {\frac{{32}}{{243}}} \right)^{ - \frac{4}{5}}}{\text{ is = ?}} \cr} " />

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$\begin{aligned} The value of \\ {(\frac{32}{243})}^{- \frac{4}{5}} is = ? \end{aligned}$ $\eqalign{ & {\text{The value of}} \cr & {\left( {\frac{{32}}{{243}}} \right)^{ - \frac{4}{5}}}{\text{ is = ?}} \cr}$

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} {(\frac{32}{243})}^{- \frac{4}{5}} \\ = {{(\frac{2}{3})}^{5}}^{- \frac{4}{5}} \\ = {(\frac{2}{3})}^{5 \times \frac{(- 4)}{5}} \\ = {(\frac{2}{3})}^{(- 4)} \\ = {(\frac{3}{2})}^{4} \\ = \frac{3^{4}}{2^{4}} \\ = \frac{81}{16} \end{aligned}

$\eqalign{ & {\left( {\frac{{32}}{{243}}} \right)^{ - \frac{4}{5}}} \cr & {\text{ = }}{\left\{ {{{\left( {\frac{2}{3}} \right)}^5}} \right\}^{ - \frac{4}{5}}} \cr & {\text{ = }}{\left( {\frac{2}{3}} \right)^{5 \times \frac{{\left( { - 4} \right)}}{5}}} \cr & {\text{ = }}{\left( {\frac{2}{3}} \right)^{\left( { - 4} \right)}} \cr & {\text{ = }}{\left( {\frac{3}{2}} \right)^4} \cr & {\text{ = }}\frac{{{3^4}}}{{{2^4}}} \cr & {\text{ = }}\frac{{81}}{{16}}{\text{ }} \cr}$

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", "text": "

\begin{aligned} The value of \\ {(\frac{32}{243})}^{- \frac{4}{5}} is  =  ? \end{aligned}

$\eqalign{ & {\text{The value of}} \cr & {\left( {\frac{{32}}{{243}}} \right)^{ - \frac{4}{5}}}{\text{ is = ?}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} {(\frac{32}{243})}^{- \frac{4}{5}} \\ = {{(\frac{2}{3})}^{5}}^{- \frac{4}{5}} \\ = {(\frac{2}{3})}^{5 \times \frac{(- 4)}{5}} \\ = {(\frac{2}{3})}^{(- 4)} \\ = {(\frac{3}{2})}^{4} \\ = \frac{3^{4}}{2^{4}} \\ = \frac{81}{16} \end{aligned}

$\eqalign{ & {\left( {\frac{{32}}{{243}}} \right)^{ - \frac{4}{5}}} \cr & {\text{ = }}{\left\{ {{{\left( {\frac{2}{3}} \right)}^5}} \right\}^{ - \frac{4}{5}}} \cr & {\text{ = }}{\left( {\frac{2}{3}} \right)^{5 \times \frac{{\left( { - 4} \right)}}{5}}} \cr & {\text{ = }}{\left( {\frac{2}{3}} \right)^{\left( { - 4} \right)}} \cr & {\text{ = }}{\left( {\frac{3}{2}} \right)^4} \cr & {\text{ = }}\frac{{{3^4}}}{{{2^4}}} \cr & {\text{ = }}\frac{{81}}{{16}}{\text{ }} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} {(\frac{32}{243})}^{- \frac{4}{5}} \\ = {{(\frac{2}{3})}^{5}}^{- \frac{4}{5}} \\ = {(\frac{2}{3})}^{5 \times \frac{(- 4)}{5}} \\ = {(\frac{2}{3})}^{(- 4)} \\ = {(\frac{3}{2})}^{4} \\ = \frac{3^{4}}{2^{4}} \\ = \frac{81}{16} \end{aligned}

$\eqalign{ & {\left( {\frac{{32}}{{243}}} \right)^{ - \frac{4}{5}}} \cr & {\text{ = }}{\left\{ {{{\left( {\frac{2}{3}} \right)}^5}} \right\}^{ - \frac{4}{5}}} \cr & {\text{ = }}{\left( {\frac{2}{3}} \right)^{5 \times \frac{{\left( { - 4} \right)}}{5}}} \cr & {\text{ = }}{\left( {\frac{2}{3}} \right)^{\left( { - 4} \right)}} \cr & {\text{ = }}{\left( {\frac{3}{2}} \right)^4} \cr & {\text{ = }}\frac{{{3^4}}}{{{2^4}}} \cr & {\text{ = }}\frac{{81}}{{16}}{\text{ }} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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