Answer
The solution is $x=\sqrt[5]{27}$
Work Step by Step
$8x^{5/3}-24=0$
Take $24$ to the right side:
$8x^{5/3}=24$
Take $8$ to divide the right side:
$x^{5/3}=\dfrac{24}{8}$
$x^{5/3}=3$
Raise both sides to $\dfrac{3}{5}$:
$(x^{5/3})^{3/5}=3^{3/5}$
$x=\sqrt[5]{3^{3}}$
$x=\sqrt[5]{27}$
