Question 150642
{{{root(5,96x^10)}}} Start with the given expression.



{{{root(5,96)*root(5,x^10)}}} Break up the root.



{{{2*root(5,3)*root(5,x^10)}}} Simplify {{{root(5,96)}}} to get {{{2*root(5,3)}}}.



*[Tex \LARGE 2\cdot\sqrt[5]{3}\left(x^{10}\right)^{\frac{1}{5}}] Rewrite the radical expression into a rational expression.



*[Tex \LARGE 2\cdot\sqrt[5]{3}x^{\left(10\right)\left(\frac{1}{5}\right)}] Multiply the exponents.



*[Tex \LARGE 2\cdot\sqrt[5]{3}x^{\left(\frac{10}{5}\right)}] Multiply



*[Tex \LARGE 2\cdot\sqrt[5]{3}x^{2}] Reduce



So {{{root(5,96x^10)}}} simplifies to {{{2x^2*root(5,3)}}}



In other words, {{{root(5,96x^10)=2x^2*root(5,3)}}}