Question 34

Jambmaths question: 

Simplify ${{81}^{\tfrac{-3}{4}}}\times {{25}^{\tfrac{1}{2}}}\times {{243}^{\tfrac{2}{5}}}$

Option A: 

$\tfrac{2}{5}$

Option B: 

$\tfrac{3}{5}$

Option C: 

$\tfrac{5}{2}$

Option D: 

$\tfrac{5}{3}$

Jamb Maths Solution: 

$\begin{align}  & {{81}^{\tfrac{-3}{4}}}\times {{25}^{\tfrac{1}{2}}}\times {{243}^{\tfrac{2}{5}}}={{3}^{4(-\tfrac{3}{4})}}\times {{5}^{2(\tfrac{1}{2})}}\times {{3}^{5(\tfrac{2}{5})}} \\ & {{81}^{\tfrac{-3}{4}}}\times {{25}^{\tfrac{1}{2}}}\times {{243}^{\tfrac{2}{5}}}={{3}^{-3}}\times 5\times {{3}^{2}} \\ & {{81}^{\tfrac{-3}{4}}}\times {{25}^{\tfrac{1}{2}}}\times {{243}^{\tfrac{2}{5}}}={{3}^{-3+2}}\times 5={{3}^{-1}}\times 5=\frac{5}{3} \\\end{align}$

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