What is \sqrt[4]{(-3)^2} ?

The solution to \sqrt[4]{(-3)^2} is sqrt(3)i

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simplify \sqrt[4]{(-3)^2}

simplify

3 i

Solution steps

Apply radical rule:

= ((- 3)^{2})^{\frac{1}{4}}

Apply exponent rule:

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

= (- 3)^{2 \cdot \frac{1}{4}}

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

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

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

= - 3

Apply radical rule:

- a = - 1 a

- 3 = - 1 3

= - 1 3

Apply imaginary number rule:

- 1 = i

= 3 i

m^{4} n^{4}

e^{- 3 t} sin (5 t)

5.32 \cdot 1 0^{- 7}

5.32 \cdot 1 0^{- 5}

(a^{2} b^{3} c) (a^{7} b c)