What is sqrt((-4)^3) ?

The solution to sqrt((-4)^3) is -8i

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simplify sqrt((-4)^3)

simplify

(- 4)^{3}

- 8 i

Solution steps

(- 4)^{3}

Apply radical rule:

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

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

Apply exponent rule:

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

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

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

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

Apply exponent rule:

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

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

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

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

= i^{3} \cdot 4^{\frac{3}{2}}

4^{\frac{3}{2}} = 8

= 8 i^{3}

i^{3} = - i

= - 8 i

3^{n} x^{n}

(\frac{x ^{2} + 4 x - 2}{x - 2}) (x - 2)

- e^{- x} \cdot 2 sec^{2} (x) tan (x)

(y^{2} - 4) (y - 2) (y - 2)

\frac{1}{2} 9.8 m^{2} (4.38 m s^{2})