Question

Evaluate : $4^{3/2}\times {125}^{-2/3}$

• A.
  $\frac{3}{25}$
• B.
  $\frac{7}{25}$
• C.
  $\frac{11}{25}$
• D.
  $\frac{8}{25}$

Answer 1

The correct option is D

$\frac{8}{25}$
$4^{3/2}\times {125}^{-2/3}=(2^2{)}^{3/2}\times (5^3{)}^{-2/3}=\left(2^{2\times \frac{3}{2}}\right)\times \left(5^{3\times \frac{-2}{3}}\right)\left(\right(a^m{)}^n=a^{m\times n})=2^3\times 5^{-2}(a^{-m}=\frac{1}{a^m})=\frac{2^3}{5^2}=\frac{8}{25}$

Hence, the answer is option D.