Question

simplify :{(243)^1/5*(25)^3/2}/{(625)^1/2*(8)^4/3*(16)^5/4}

Answer 1

$Simplify \: \: \frac{ {(243)}^{ \frac{1}{5} } \times {(25)}^{ \frac{3}{2} } }{ {(625)}^{ \frac{1}{2} } \times {(8)}^{ \frac{4}{3} } \times {(16)}^{ \frac{5}{4} } } \\ \\ \\ Solution \: \: \: : \\ \\ = \frac{ {(243)}^{ \frac{1}{5} } \times {(25)}^{ \frac{3}{2} } }{ {(625)}^{ \frac{1}{2} } \times {(8)}^{ \frac{4}{3} } \times {(16)}^{ \frac{5}{4} } } \\ \\ \\ = \frac{ {(3)}^{5 \times \frac{1}{5} } \times {(5)}^{2 \times \frac{3}{2} } }{ {(25)}^{2 \times \frac{1}{2} } \times {(2)}^{3 \times \frac{4}{3} } \times {(2)}^{4 \times \frac{5}{4} } } \\ \\ \\ = \frac{3 \times {(5)}^{3} }{25 \times {(2)}^{4} \times {(2)}^{5} } \\ \\ \\ = \frac{3 \times {(5)}^{3} }{ {(5)}^{2} \times {(2)}^{4 + 5} } \\ \\ \\ = \frac{3 \times {(5)}^{3} }{ {(5)}^{2} \times {(2)}^{9} } \\ \\ \\ = \frac{3 \times {(5)}^{3 - 2} }{ {(2)}^{9} } \\ \\ \\ = \frac{3 \times 5}{ {(2)}^{9} } \\ \\ \\ = \frac{15}{512}$