Answer: [tex]2xy^3\\\\[/tex]
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Work Shown:
[tex]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\\\\[/tex]
An alternative method is this
[tex]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}\\\\[/tex]
