 # Rewrite with rational exponents. (root(13)(7x^2 y))^3 Flambergru 2022-08-04 Answered
Rewrite with rational exponents.
$\left(\sqrt{7{x}^{2}y}{\right)}^{3}$
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$\left(\sqrt{7{x}^{2}y}{\right)}^{3}=\left[\left(7{x}^{2}y{\right)}^{1/13}{\right]}^{3}$ [As$\sqrt[y]{x}={x}^{1/y}$]
$=\left(7{x}^{2}y{\right)}^{\left(1/13\right)\ast 3}$ [As $\left({A}^{x}{\right)}^{y}={A}^{x\ast y}$]
$=\left(7{x}^{2}y{\right)}^{3/13}$
$=\left(7{\right)}^{3/13}\ast \left({x}^{2}{\right)}^{3/13}\ast \left(y{\right)}^{3/13}$
$=\left(7{\right)}^{3/13}\ast \left(x{\right)}^{2\ast 3/13}\ast \left(y{\right)}^{3/13}$
$=\left(7{\right)}^{3/13}\ast \left(x{\right)}^{6/13}\ast \left(y{\right)}^{3/13}$
Answer:- $\left(7{\right)}^{3/13}\ast \left(x{\right)}^{6/13}\ast \left(y{\right)}^{3/13}$
###### Not exactly what you’re looking for? Jaylyn Gibson
$\left(\sqrt{\sqrt{7{x}^{2}y}}{\right)}^{3}﻿=\left(7{x}^{2}y{\right)}^{3/13}=7{x}^{6/13}{y}^{3/13}$