What is (sqrt(xy))/(\sqrt[4]{81xy)} ?

The solution to (sqrt(xy))/(\sqrt[4]{81xy)} is (\sqrt[4]{xy})/3

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simplify (sqrt(xy))/(\sqrt[4]{81xy)}

simplify

\frac{x y}{4 81 x y}

\frac{4 x y}{3}

Solution steps

\frac{x y}{4 81 x y}

Simplify

4 81 x y : 3 4 x y

= \frac{x y}{3 4 x y}

Apply radical rule:

a = a^{\frac{1}{2}}

x y = (x y)^{\frac{1}{2}}

= \frac{( x y ) ^{\frac{1}{2}}}{3 4 x y}

Apply radical rule:

n a = a^{\frac{1}{n}}

4 x y = (x y)^{\frac{1}{4}}

= \frac{( x y ) ^{\frac{1}{2}}}{3 ( x y ) ^{\frac{1}{4}}}

Simplify

\frac{( x y ) ^{\frac{1}{2}}}{( x y ) ^{\frac{1}{4}}} : 4 x y

= \frac{4 x y}{3}

\frac{x}{2} > \frac{1}{3}

x^{2} - 11 x y + 30 y^{2}

(6 a^{\frac{4}{3}} \cdot 2 b^{\frac{1}{4}}) (a^{\frac{1}{3}} \cdot 4 b^{\frac{1}{8}})

\frac{8 !}{4 ! 4 !}

v^{2} = 0 + 2 \cdot 2.11 \cdot 5.84

What is (sqrt(xy))/(\sqrt[4]{81xy)} ?
The solution to (sqrt(xy))/(\sqrt[4]{81xy)} is (\sqrt[4]{xy})/3