What is \sqrt[4]{-1}^6 ?

The solution to \sqrt[4]{-1}^6 is -i

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simplify \sqrt[4]{-1}^6

simplify

- i

Solution steps

Apply radical rule:

= ((- 1)^{\frac{1}{4}})^{6}

Apply exponent rule:

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

= (- 1)^{\frac{1}{4} \cdot 6}

\frac{1}{4} \cdot 6 = \frac{3}{2}

= (- 1)^{\frac{3}{2}}

Apply exponent rule:

a^{\frac{m}{n}} = (a^{\frac{1}{n}})^{m}

(- 1)^{\frac{3}{2}} = (- 1)^{3}

= (- 1)^{3}

Apply imaginary number rule:

- 1 = i

= i^{3}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

i^{3} = i^{2} i

= i^{2} i

Apply imaginary number rule:

i^{2} = - 1

= - 1 i

Multiply:

1 i = i

= - i

0.021 \cdot 4 \cdot 1 0^{- 3}

e^{- 2 (5.25)}

0.0365 \cdot ((0.083145 \cdot 305)^{- 2})

e^{1} e^{2}

m^{2} n^{2} (m - n)