Answer
$1$
Work Step by Step
Factor the radicands so that we can take the cube roots of the numerator and the square roots of the denominator later:
$=\dfrac {\sqrt[3] {2^3 \cdot x^{3} \cdot x^{3} \cdot y^{3} \cdot y^{3} \cdot y^{3} \cdot y^{3}}}{\sqrt {2^{2} \cdot x^{2} \cdot x^{2} \cdot y^{2} \cdot y^{2} \cdot y^{2} \cdot y^{2}}}$
Take the cube roots of the numerator and the square roots of the denominator:
$=\dfrac {2 \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y }{2 \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y}$
Simplify by canceling similar factors in the numerator and denominator:
$=\dfrac{1}{1}$
Simplify:
$=1$
