Question 152334
{{{sqrt(54xy^7)/sqrt(6xy)}}} Start with the given expression.



{{{sqrt((54xy^7)/(6xy))}}} Combine the roots.



{{{sqrt(9y^6)}}} Divide {{{(54xy^7)/(6xy)}}} to get {{{(54xy^7)/(6xy)=(54/6)((xy^7)/(6xy))=9x^(1-1)y^(7-1)=9x^0y^6=9y^6}}}.



*[Tex \LARGE \left(9y^6\right)^{\frac{1}{2}}] Convert from radical notation to exponent notation.



*[Tex \LARGE \left(\left(9\right)^1y^6\right)^{\frac{1}{2}}] Rewrite *[Tex \LARGE 9] as *[Tex \LARGE \left(9\right)^1].



*[Tex \LARGE \left(9\right)^{\left(1\right)\left(\frac{1}{2}\right)}y^{\left(6\right)\left(\frac{1}{2}\right)}] Multiply the outer exponent by each of the inner exponents.



*[Tex \LARGE \left(9\right)^{\frac{1}{2}}y^{3}] Multiply the exponents.



{{{sqrt(9)y^3}}} Convert back to radical notation



{{{3y^3}}} Take the square root of 9 to get 3



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Answer:


So {{{sqrt(54xy^7)/sqrt(6xy)}}} simplifies to {{{3y^3}}}



In other words, {{{sqrt(54xy^7)/sqrt(6xy)=3y^3}}} where every variable is positive, {{{x<>0}}}, and {{{y<>0}}}