Answer
$\dfrac{9}{4} $
Work Step by Step
Use the rule $a^{-m}=\left(\dfrac{1}{a}\right)^m$:
$\left (\dfrac{8}{27} \right )^{-\frac{2}{3}}=\left (\dfrac{27}{8} \right )^{\frac{2}{3}}$
Use $27=3^3$ and $8=2^3$.
$=\left (\dfrac{3^3}{2^3} \right )^{\frac{2}{3}}$
Use the rule $\left(\dfrac{a}{b}\right)^n=\dfrac{a^m}{b^m}$:
$=\dfrac{(3^3)^{\frac{2}{3}}}{(2^3)^{\frac{2}{3}}} $
Use the rule $\left(a^m\right)^n=a^{mn}$, then simplify to obtain:
$=\dfrac{3^{3\cdot \frac{2}{3}}}{2^{3\cdot \frac{2}{3}}} $
$=\dfrac{3^{2}}{2^{2}} $
$=\dfrac{9}{4} $
Hence, the correct answer is $\frac{9}{4} $.
