Question

simplify.
$\sqrt[4]{16 {x}^{4} {y}^{12} }$
assume all variables are non negative
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Answer 1

Answer:  $2xy^3$

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Work Shown:

$z = \sqrt[4]{16x^4y^{12}}\\\\z = \sqrt[4]{2^4*x^4*(y^3)^4}\\\\z = \sqrt[4]{(2xy^3)^4}\\\\z = 2xy^3$

An alternative method is this

$z = \sqrt[4]{16x^4y^{12}}\\\\z = \sqrt[4]{16}\sqrt[4]{x^4}\sqrt[4]{y^{12}}\\\\z = \sqrt[4]{2^4}\sqrt[4]{x^4}\sqrt[4]{y^{12}}\\\\z = 2^{4/4}x^{4/4}y^{12/4}\\\\z = 2^{1}x^{1}y^{3}\\\\z = 2xy^{3}$