Question

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$\huge \frac{ {(25)}^{ \frac{3}{2} } \times {(243)}^{ \frac{3}{5} } }{(16) \frac{5}{4} \times {(8)}^{ \frac{4}{3} } }$
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Answer is
$\frac{3375}{512}$
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Answer 1

Explanation:

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Answer 2

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According to question:-

$\huge = \frac{ {25}^{ \frac{3}{2} } \times {243}^{ \frac{3}{5} } }{ {16}^{ \frac{5}{4} } \times {8}^{ \frac{4}{3} } }$

$\huge= \frac{ {( {5}^{2} })^{ \frac{3}{2} } \times { {(3}^{5} })^{ \frac{3}{5} } }{ { {(2}^{4} })^{ \frac{5}{4} } \times { {(2}^{4} })^{ \frac{4}{3} } }$

$\huge= \frac{ {5}^{2 \times \frac{3}{2} } \times {3}^{5 \times \frac{3}{5} } }{ {2}^{4 \times \frac{5}{4} } \times {2}^{3 \times \frac{4}{3} } }$

$\huge = \frac{ {5}^{3} \times {3}^{3} }{ {2}^{5} \times {2}^{4} }$

$\huge = \frac{125 \times 27}{32 \times 16}$

$\huge = \frac{3375}{512}$

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