Question

what is (5√8)^5/2 * 16^(-3)/2 ?

Answer 1

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$( \sqrt[5]{8} ) ^{ \frac{5}{2} } \times (16) ^{ \frac{ - 3}{2} }$

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$( \sqrt[5]{8} ) ^{ \frac{5}{2} } \times (16) ^{ \frac{ - 3}{2} } \\ = (8 ^{ \frac{1}{5} } ) ^{ \frac{5}{2} } \times ( {2}^{4} ) ^{ \frac{ - 3}{2} } \\ = {8}^{ \frac{1}{5} \times \frac{5}{2} } \times {2}^{4 \times \frac{ - 3}{2} } \\ = {8}^{ \frac{1}{2} } \times {2}^{ - 6} \\ = ({2}^{3 } ) ^{ \frac{1}{2} } \times {2}^{ - 6} \\ = {2}^{ \frac{3}{2} } \times {2}^{ - 6} \\ = {2}^{ \frac{3}{2} + ( - 6)} \\ = {2}^{ \frac{3 - 12}{2} } \\ {2}^{ \frac{ - 9}{2} }$

$\huge\fcolorbox{blue}{green}{hope \: it \: helps \: u}$