Question

simplify the following expression.
$sqrt{x^{5}y^{5}} \cdot 4sqrt{2x^{13}y^{4}}$
$sqrt{x^{5}y^{5}} \cdot 4sqrt{2x^{13}y^{4}} = \square$
(simplify your answer. type an exact answer, using radicals as needed

Explanation:

Step1: Combine the radical terms

$\sqrt{x^5y^5} \cdot 4\sqrt{2x^{13}y^4} = 4\sqrt{x^5y^5 \cdot 2x^{13}y^4}$

Step2: Multiply inside the radical

$4\sqrt{2 \cdot x^{5+13} \cdot y^{5+4}} = 4\sqrt{2x^{18}y^9}$

Step3: Simplify the radical

$4\sqrt{x^{18}y^8 \cdot 2y} = 4x^9y^4\sqrt{2y}$

Answer:

$4x^9y^4\sqrt{2y}$