Answer
$\color{blue}{-\dfrac{2}{3}}$
Work Step by Step
RECALL:
(1) $a^{1/n} = \sqrt[n]{a}$
(2) If $a \gt 0$, then $\sqrt[n]{a^n} = a$
(3) If $n$ is odd, then $\sqrt[n]{a^n}=a$
Use rule (1) above to obtain:
$\left(-\dfrac{8}{27}\right)^{1/3} = \sqrt[3]{-\left(\dfrac{8}{27}\right)}$
Since $-\dfrac{8}{27}=\left(-\dfrac{2}{3}\right)^3$, then the expression above is equivalent to:
$=\sqrt[3]{\left(-\dfrac{2}{3}\right)^3}$
Use rule (3) above to simplify and have:
$\sqrt[3]{\left(-\dfrac{2}{3}\right)^3}=\color{blue}{-\dfrac{2}{3}}$
