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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