Question

given all variables below are positive, express in simplest radical form with a rational denominator.
$\frac{sqrt{64x^{13}y^{4}}}{sqrt{2x^{4}y}}$

Explanation:

Step1: Combine radicals into one

$\frac{\sqrt{64x^{13}y^4}}{\sqrt{2x^4y}} = \sqrt{\frac{64x^{13}y^4}{2x^4y}}$

Step2: Simplify the fraction inside

$\sqrt{32x^{9}y^{3}}$

Step3: Factor into perfect squares

$\sqrt{16 \cdot 2 \cdot x^8 \cdot x \cdot y^2 \cdot y}$

Step4: Extract perfect square roots

$4x^4y\sqrt{2xy}$

Answer:

$4x^4y\sqrt{2xy}$