waecmaths question:
Solve ${{\left( \frac{27}{125} \right)}^{-\tfrac{1}{3}}}\times {{\left( \frac{4}{9} \right)}^{\tfrac{1}{2}}}$
Option A:
$\tfrac{10}{9}$
Option B:
$\tfrac{9}{10}$
Option C:
$\tfrac{2}{5}$
Option D:
$\tfrac{12}{125}$
waecmaths solution:
$\begin{align} & {{\left( \frac{27}{125} \right)}^{-\tfrac{1}{3}}}\times {{\left( \frac{4}{9} \right)}^{\tfrac{1}{2}}}={{\left( {{\left( \frac{27}{125} \right)}^{\tfrac{1}{3}}} \right)}^{-1}}\times {{\left( \frac{4}{9} \right)}^{\tfrac{1}{2}}} \\ & ={{\left( \frac{{{({{3}^{3}})}^{\tfrac{1}{3}}}}{{{({{5}^{3}})}^{\tfrac{1}{3}}}} \right)}^{-1}}\times \frac{{{({{2}^{2}})}^{\tfrac{1}{2}}}}{{{({{3}^{2}})}^{\tfrac{1}{2}}}} \\ & ={{\left( \frac{3}{5} \right)}^{-1}}\times \frac{2}{3} \\ & =\frac{5}{3}\times \frac{2}{3}=\frac{10}{9} \end{align}$
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