Question

If $\frac{{\left(\frac{1}{216}\right)}^{\frac{-2}{3}}}{{\left(\frac{1}{27}\right)}^{\frac{-4}{3}}}=x$, the value of x is

• A. $\frac{3}{4}$
• B. $\frac{4}{9}$
• C. $\frac{2}{3}$
• D. $\frac{1}{8}$

Answer 1

The correct option is B $\frac{4}{9}$

$\Rightarrow \frac{{\left(\frac{1}{216}\right)}^{\frac{-2}{3}}}{{\left(\frac{1}{27}\right)}^{\frac{-4}{3}}}$$\Rightarrow \frac{{\left({\left(\frac{1}{6}\right)}^3\right)}^{\frac{-2}{3}}}{{\left({\left(\frac{1}{3}\right)}^3\right)}^{\frac{-4}{3}}}$
$\Rightarrow \frac{\frac{1}{6^{-2}}}{\frac{1}{3^{-4}}}$
$\Rightarrow \frac{6^2}{3^4}\Rightarrow \frac{36}{81}\Rightarrow \frac{4}{9}$