Question

Evaluate the following expression:
${\left(\frac{4}{9}\right)}^{-\frac{3}{2}}$

• A. $\frac{2}{3}$
• B. $\frac{2}{9}$
• C. $\frac{3}{16}$
• D. $\frac{27}{8}$

Answer 1

The correct option is D $\frac{27}{8}$

$\frac{27}{3}:{\left(\frac{4}{9}\right)}^{-\frac{3}{2}}={\left(\frac{9}{4}\right)}^{\frac{3}{2}}=\sqrt{{\left(\frac{9}{4}\right)}^3}={\left(\sqrt{\left(\frac{9}{4}\right)}\right)}^3=\frac{3^3}{2^3}=\frac{27}{8}$