Question 39

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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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