Question 152886
{{{root(4,81x^4y^(20))}}} Start with the given expression.



*[Tex \LARGE \left(81x^4y^{20}\right)^{\frac{1}{4}}] Rewrite the radical expression into exponential form.



*[Tex \LARGE \left(\left(81\right)^1x^4y^{20}\right)^{\frac{1}{4}}] Rewrite *[Tex \LARGE 81] as *[Tex \LARGE \left(81\right)^1].



*[Tex \LARGE \left(81\right)^{\left(1\right)\left(\frac{1}{4}\right)}x^{\left(4\right)\left(\frac{1}{4}\right)}y^{\left(20\right)\left(\frac{1}{4}\right)}] Multiply the outer exponent by each of the inner exponents.



*[Tex \LARGE \left(81\right)^{\frac{1}{4}}x^{\frac{4}{4}}y^{\frac{20}{4}}] Multiply the exponents.




*[Tex \LARGE \left(81\right)^{\frac{1}{4}}x^{1}y^{5}] Reduce.



{{{root(4,81)(xy^5)}}} Convert back to radical notation.



{{{3xy^5}}} Take the fourth root of *[Tex \LARGE 81] to get *[Tex \LARGE 3]



So {{{root(4,81x^4y^(20))=3xy^5}}} where every variable is positive.