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

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

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

\frac{2}{17}

e^{- t} e^{t}

7.5 \cdot 1 0^{- 7}

7.5 \cdot 1 0^{- 2}

- 6 e^{- 3}

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