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Popular >

simplify (\sqrt[4]{-16})^2

Solution

simplify

Solution

4 i

Solution steps

Apply radical rule:

= ((- 16)^{\frac{1}{4}})^{2}

Apply exponent rule:

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

= (- 16)^{\frac{1}{4} \cdot 2}

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

= (- 16)^{\frac{1}{2}}

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

= - 16

Apply radical rule:

- a = - 1 a

- 16 = - 1 16

= - 1 16

Apply imaginary number rule:

- 1 = i

= 16 i

16 = 4

= 4 i

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Frequently Asked Questions (FAQ)

What is (\sqrt[4]{-16})^2 ?
The solution to (\sqrt[4]{-16})^2 is 4i