What is \sqrt[4]{(-2)^2} ?

The solution to \sqrt[4]{(-2)^2} is sqrt(2)i

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simplify \sqrt[4]{(-2)^2}

simplify

2 i

Solution steps

Apply radical rule:

= ((- 2)^{2})^{\frac{1}{4}}

Apply exponent rule:

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

= (- 2)^{2 \cdot \frac{1}{4}}

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

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

a^{\frac{1}{2}} = a

= - 2

Apply radical rule:

- a = - 1 a

- 2 = - 1 2

= - 1 2

Apply imaginary number rule:

- 1 = i

= 2 i

e^{- 2.4} \cdot 38

- a^{5} b^{5} c^{2}

(e^{3 x})^{\frac{1}{6}}

0.5 ((x)^{2})^{0.5}

(8.9925 \cdot 1 0^{- 4}) \cdot 2