What is sqrt((-5)^3) ?

The solution to sqrt((-5)^3) is 5sqrt(5)i

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simplify sqrt((-5)^3)

simplify

(- 5)^{3}

55 i

Solution steps

(- 5)^{3}

(- 5)^{3} = - 125

= - 125

Prime factorization of

125 : 5^{3}

= - 5^{3}

Apply exponent rule:

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

- 5^{3} = - 5^{2} \cdot 5

= - 5^{2} \cdot 5

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

- 5^{2} \cdot 5 = 5^{2} - 5

= 5^{2} - 5

Apply radical rule:

a^{2} = a, a \geq 0

5^{2} = 5

= 5 - 5

Apply radical rule:

- a = a - 1

- 5 = 5 - 1

= 55 - 1

Apply imaginary number rule:

- 1 = i

= 55 i

e^{- (x + 1)}

\frac{6 , 0 \cdot 1 0 ^{24} \cdot 50}{640 0 ^{2}} \cdot 6.67 \cdot 1 0^{- 11}

(4 a^{2}) (6 a^{2})

- \frac{1}{3} e^{- 3 (0)}