Question

simplify :- (81/16)^-3/4×[(9/25)^3/2÷(5/2)^-3]

Answer 1

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Answer 2

81 = $3^{4}$
16 = $2^{4}$
25 = $5^{2}$
9 = $3^{2}$
$(\frac{81}{16})^{-3/4}$×[$(\frac{9}{25})^{3/2}$÷$(\frac{5}{2})^{-3}$] = [tex](\frac{ 3^{4} }{2^{4}})^{-3/4}[\[(\frac{3^{2}}{5^{2}})^{3/2} \div (\frac{5}{2})^{-3}] \\ [/tex]
                       = $(\frac{ 3^{-3}}{2^{-3}})[\[\frac{3^{3}2^{-3}}{5^{3}5^{-3}}]$
                       = 1