Question

simplify (3/4)^4 (8/5)^-12 (32/5)^6​

Answer 1

Correct Question's Answer :-

$\purple{ \bf{ \bigg( \dfrac{3}{5} \bigg) ^{4} \times \bigg( \dfrac{8}{5} \bigg) ^{ - 12} × \bigg( \dfrac{32}{5} \bigg) ^{6} }}$

$\tt{ \Rightarrow \: \dfrac{ {3}^{4} }{ {5}^{4} } \times \bigg( \dfrac{5}{8} \bigg) ^{12} \times \dfrac{(32 {)}^{6} }{ {5}^{6} } }$

$\tt{ \Rightarrow \: \dfrac{ {3}^{4} }{ {5}^{4} } \times \bigg( \dfrac{5}{8} \bigg) ^{12} \times \dfrac{( {2}^{5} {)}^{6} }{ {5}^{6} } }$

$\tt{ \Rightarrow \: \dfrac{81}{ {5}^{4} } \times \dfrac{ {5}^{12} }{ {8}^{12} } \times \dfrac{ {2}^{30} }{ {5}^{6} } }$

$\tt{ \Rightarrow \: \dfrac{81 \times {5}^{12} \times {2}^{30} }{ {5}^{4 + 6} \times ( {2}^{3} {)}^{12} } }$

$\tt{ \Rightarrow \: \dfrac{81 \times {5}^{12} \times {2}^{30} }{ {5}^{10} \times {2}^{36} } }$

$\tt{ \Rightarrow \: \dfrac{81 \times {5}^{12 - 10} }{ {2}^{36 - 30} } }$

$\tt{ \Rightarrow \: \dfrac{81 \times {5}^{2} }{ {2}^{6} } }$

$\tt{ \Rightarrow \: \dfrac{81 \times 25}{64} }$

$\purple{ \bf{ \Rightarrow \: \dfrac{2025}{64} }}$

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