What is \sqrt[5]{sqrt((-1)/5)} ?

The solution to \sqrt[5]{sqrt((-1)/5)} is \sqrt[10]{-1}\sqrt[10]{1/5}

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simplify \sqrt[5]{sqrt((-1)/5)}

simplify

Solution steps

Apply radical rule:

= ((\frac{- 1}{5})^{\frac{1}{2}})^{\frac{1}{5}}

Apply exponent rule:

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

= (\frac{- 1}{5})^{\frac{1}{2} \cdot \frac{1}{5}}

\frac{1}{2} \cdot \frac{1}{5} = \frac{1}{10}

= (\frac{- 1}{5})^{\frac{1}{10}}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

Apply radical rule:

1 0^{- 4.76}

(5 x^{4}) (9 x^{6})

1000 (1 - 0.006)^{- 10}

What is \sqrt[5]{sqrt((-1)/5)} ?
The solution to \sqrt[5]{sqrt((-1)/5)} is \sqrt[10]{-1}\sqrt[10]{1/5}