What is (\sqrt[6]{5xy^5})^5 ?

The solution to (\sqrt[6]{5xy^5})^5 is 5^{5/6}(xy^5)^{5/6}

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simplify (\sqrt[6]{5xy^5})^5

simplify

5^{\frac{5}{6}} (x y^{5})^{\frac{5}{6}}

Solution steps

Apply radical rule:

= ((5 x y^{5})^{\frac{1}{6}})^{5}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (5 x y^{5})^{\frac{1}{6} \cdot 5}

\frac{1}{6} \cdot 5 = \frac{5}{6}

= (5 x y^{5})^{\frac{5}{6}}

Apply exponent rule:

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

= 5^{\frac{5}{6}} (x y^{5})^{\frac{5}{6}}

e^{- \frac{4}{4}}

e^{- 2.28874135}

2 x (x x - 1) (\frac{x}{2 x - 1} + x - 1)

(\frac{1}{3}) e^{- 3 (\frac{1}{3})}

1296

What is (\sqrt[6]{5xy^5})^5 ?
The solution to (\sqrt[6]{5xy^5})^5 is 5^{5/6}(xy^5)^{5/6}