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Popular >

simplify (\sqrt[4]{-1})^5

Solution

simplify

Solution

Solution steps

Apply radical rule:

= ((- 1)^{\frac{1}{4}})^{5}

Apply exponent rule:

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

= (- 1)^{\frac{1}{4} \cdot 5}

\frac{1}{4} \cdot 5 = \frac{5}{4}

= (- 1)^{\frac{5}{4}}

(- 1)^{\frac{5}{4}} = (- 1)^{1 + \frac{1}{4}}

= (- 1)^{1 + \frac{1}{4}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= (- 1)^{1} (- 1)^{\frac{1}{4}}

Refine

Remove parentheses:

(- a) = - a

Multiply:

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Frequently Asked Questions (FAQ)

What is (\sqrt[4]{-1})^5 ?
The solution to (\sqrt[4]{-1})^5 is -\sqrt[4]{-1}