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Step-by-step explanation:
[tex] \bf \underline{Given-} \\ [/tex]
[tex] \sf{ \bigg( \frac{3}{5} \bigg) ^{4} \times \bigg( \frac{8}{5} \bigg) ^{ - 12} ×\bigg( \frac{32}{5} \bigg) ^{6} }[/tex]
[tex] \bf \underline{To\: find-} \\ [/tex]
[tex]\textsf{Simplifying form = ?}\\[/tex]
[tex] \bf \underline{Solution-} \\ [/tex]
[tex]\textsf{Given fractional expression,}\\[/tex]
[tex] \sf{ \bigg( \frac{3}{5} \bigg) ^{4} \times \bigg( \frac{8}{5} \bigg) ^{ - 12} × \bigg( \frac{32}{5} \bigg) ^{6} }[/tex]
[tex] \sf{ \Rightarrow \: \frac{ {3}^{4} }{ {5}^{4} } \times \bigg( \frac{5}{8} \bigg) ^{12} \times \frac{(32 {)}^{6} }{ {5}^{6} } } \\ [/tex]
[tex] \sf{ \Rightarrow \: \frac{ {3}^{4} }{ {5}^{4} } \times \bigg( \frac{5}{8} \bigg) ^{12} \times \frac{( {2}^{5} {)}^{6} }{ {5}^{6} } } \\ [/tex]
[tex] \sf{ \Rightarrow \: \frac{81}{ {5}^{4} } \times \frac{ {5}^{12} }{ {8}^{12} } \times \frac{ {2}^{30} }{ {5}^{6} } } \\ [/tex]
[tex] \sf{ \Rightarrow \: \frac{81 \times {5}^{12} \times {2}^{30} }{ {5}^{4 + 6} \times ( {2}^{3} {)}^{12} } } \\ [/tex]
[tex] \sf{ \Rightarrow \: \frac{81 \times {5}^{12} \times {2}^{30} }{ {5}^{10} \times {2}^{36} } } \\ [/tex]
[tex] \sf{ \Rightarrow \: \frac{81 \times {5}^{12 - 10} }{ {2}^{36 - 30} } } \\ [/tex]
[tex] \sf{ \Rightarrow \: \frac{81 \times {5}^{2} }{ {2}^{6} } } \\ [/tex]
[tex] \sf{ \Rightarrow \: \frac{81 \times 25}{64} } \\ [/tex]
[tex] \sf{ \Rightarrow \: \frac{2025}{64} } \\ [/tex]
[tex] \bf \underline{Answer-} \\ [/tex]
[tex] \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} }.} \\ [/tex]