Math, asked by prafulgopi2005, 9 months ago

Simplify 3/ 5^ 4 × 8/ 5 ^ −12 x 32/ 5 ^ 6

Answers

Answered by shalinisudha0268
1

Answer:

300000000....

your answer

Answered by Salmonpanna2022
1

Step-by-step explanation:

 \bf \underline{Given-} \\

 \sf{ \bigg( \frac{3}{5}   \bigg) ^{4} \times  \bigg( \frac{8}{5}  \bigg) ^{ - 12}   ×\bigg( \frac{32}{5} \bigg) ^{6} }

 \bf \underline{To\: find-} \\

\textsf{Simplify the given fractional expression and find their value.}\\

 \bf \underline{Solution-} \\

\textsf{Given fractional expression,}\\

 \sf{ \bigg( \frac{3}{5}   \bigg) ^{4} \times  \bigg( \frac{8}{5}  \bigg) ^{ - 12}  × \bigg( \frac{32}{5} \bigg) ^{6} }

 \sf{ \Rightarrow \: \frac{ {3}^{4} }{ {5}^{4} } \times  \bigg( \frac{5}{8}   \bigg) ^{12}   \times  \frac{(32 {)}^{6} }{ {5}^{6} } }  \\

 \sf{ \Rightarrow \: \frac{ {3}^{4} }{ {5}^{4} }   \times \bigg( \frac{5}{8} \bigg) ^{12}   \times  \frac{( {2}^{5}  {)}^{6} }{ {5}^{6} }   }  \\

 \sf{ \Rightarrow \:  \frac{81}{ {5}^{4} }  \times  \frac{ {5}^{12} }{ {8}^{12} } \times  \frac{ {2}^{30} }{ {5}^{6} }  }  \\

 \sf{ \Rightarrow \: \frac{81 \times  {5}^{12}  \times  {2}^{30} }{ {5}^{4 + 6}  \times ( {2}^{3}  {)}^{12} }  }  \\

 \sf{ \Rightarrow \: \frac{81 \times  {5}^{12}  \times  {2}^{30} }{ {5}^{10}  \times  {2}^{36} }  }  \\

 \sf{ \Rightarrow \: \frac{81 \times  {5}^{12 - 10} }{ {2}^{36 - 30} } } \\

 \sf{ \Rightarrow \: \frac{81 \times  {5}^{2} }{ {2}^{6} } } \\

 \sf{ \Rightarrow \: \frac{81 \times 25}{64} } \\

 \sf{ \Rightarrow \: \frac{2025}{64} } \\

 \bf \underline{Answer-} \\

 \bf{\underline{{Hence, the \:  value  \: of  : \:  \bigg( \frac{3}{5}   \bigg) ^{4} \times  \bigg( \frac{8}{5}  \bigg) ^{ - 12}   ×\bigg( \frac{32}{5} \bigg) ^{6} }  \: is \:  \frac{2025}{64} }.} \\

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