What is sqrt(\sqrt[7]{xy)}\times sqrt(xy) ?

The solution to sqrt(\sqrt[7]{xy)}\times sqrt(xy) is \sqrt[7]{x^4}\sqrt[7]{y^4}

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simplify sqrt(\sqrt[7]{xy)}\times sqrt(xy)

simplify

Solution steps

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

= (x y)^{\frac{1}{14}} (x y)^{\frac{1}{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

(x y)^{\frac{1}{14}} (x y)^{\frac{1}{2}} = (x y)^{\frac{1}{14} + \frac{1}{2}}

= (x y)^{\frac{1}{14} + \frac{1}{2}}

\frac{1}{14} + \frac{1}{2} = \frac{4}{7}

= (x y)^{\frac{4}{7}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(x y)^{\frac{4}{7}} = x^{\frac{4}{7}} y^{\frac{4}{7}}

= x^{\frac{4}{7}} y^{\frac{4}{7}}

(2 r^{3} s^{2}) (4 r^{2} s^{5})

(2 e^{2 x}) (e^{x})

(- 4^{4} y^{3}) x^{3} x^{2} y x (- 6 x y^{4})

e^{- \frac{1}{2} l n ∣ x ∣}

What is sqrt(\sqrt[7]{xy)}\times sqrt(xy) ?
The solution to sqrt(\sqrt[7]{xy)}\times sqrt(xy) is \sqrt[7]{x^4}\sqrt[7]{y^4}