What is 5^{1/5}((-1)^{2/(5pi)})^{1/5} ?

The solution to 5^{1/5}((-1)^{2/(5pi)})^{1/5} is 5^{1/5}((-1)^{2/(5pi)})^{1/5}

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simplify 5^{1/5}((-1)^{2/(5pi)})^{1/5}

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

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

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

Apply exponent rule:

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

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

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What is 5^{1/5}((-1)^{2/(5pi)})^{1/5} ?
The solution to 5^{1/5}((-1)^{2/(5pi)})^{1/5} is 5^{1/5}((-1)^{2/(5pi)})^{1/5}