Question

Simplify: $(81/16{)}^{-3/4}\times \left[\right(25/9{)}^{-3/2}÷\left(5/2{)}^{-3}\right]$

Answer 1

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

$=(\frac{2}{3}{)}^3\times [(\frac{3}{5}{)}^3÷(\frac{2}{5}{)}^3]=(\frac{2^3}{3^3})\times (\frac{3^3}{5^3})\times (\frac{5^3}{2^3})=1$