Question

Evaluate $(\frac{27}{125}{)}^{\frac{2}{3}}\times (\frac{9}{25}{)}^{\frac{-3}{2}}$

• A. 0.00009
• B. 0.000009
• C. 90 × 10^-4
• D. 0.009 × 10^-4

Answer 1

The correct option is A

0.00009

Given $(\frac{27}{125}{)}^{\frac{2}{3}}\times (\frac{9}{25}{)}^{\frac{-3}{2}}$

$=(\frac{3^3}{5^3}{)}^{\frac{2}{3}}\times (\frac{3^2}{5^2}{)}^{\frac{-3}{2}}$

$=\left(\right(\frac{3}{5}{)}^3{)}^{\frac{2}{3}}\times \left(\right(\frac{3}{5}{)}^2{)}^{\frac{-3}{2}}$

$\because \left(\right(a{)}^m{)}^n=a^{(m\times n)}$

$\Rightarrow$ $(\frac{3}{5}{)}^2\times (\frac{3}{5}{)}^{-3}$

$\because a^m\times a^n=a^{(m+n)}$

$\Rightarrow$ $(\frac{3}{5}{)}^{-1}$

$\Rightarrow$ $\frac{5}{3}$