Question

$\frac{3}{5}^{3} \times \frac{5}{4}^{4} \times \frac{4}{3} ^{5}$
Evaluate the following.
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Answer 1

Appropriate Question :

$\sf \looparrowright(\frac{3}{5})^{3} \times (\frac{5}{4})^{4} \times( \frac{4}{3}) ^{5}$

Solution :

$\sf (\frac{3}{5})^{3} \times (\frac{5}{4})^{4} \times (\frac{4}{3}) ^{5}$

$\sf \leadsto \frac{ {3}^{3} }{ {5}^{3} } \times \frac{ {5}^{4} }{ {4}^{4} } \times \frac{ {4}^{5} }{ {3}^{5} }$

We will break-down the powers for getting it easier

$\sf \leadsto \frac{ {3}^{3} }{ {5}^{3} } \times \frac{ {5}^{3} \times {5}^{1} }{ {4}^{4} } \times \frac{ {4}^{4} \times {4}^{1} }{ {3}^{3} \times {3}^{2} }$

$\sf \leadsto \frac{ \cancel{ {3}^{3}} }{ \cancel{ {5}^{3} }} \times \frac{ \cancel{ {5}^{3}} \times {5}^{1} }{ \cancel{ {4}^{4} }} \times \frac{ \cancel{{4}^{4}} \times {4}^{1} }{ \cancel{ {3}^{3} }\times {3}^{2} }$

$\leadsto \sf5 \times \frac{4}{ {3}^{2} }$

$\sf \leadsto \frac{5 \times 4}{9}$

$\leadsto \sf \frac{20}{9}$

$\sf \leadsto 1\frac{2}{9}$

$\dag \: \sf so \: the \: answer \: is \: \small \boxed{ 1\frac{2}{9} } \: \dag$