What is sqrt((-2)^3) ?

The solution to sqrt((-2)^3) is 2sqrt(2)i

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simplify sqrt((-2)^3)

simplify

(- 2)^{3}

22 i

Solution steps

(- 2)^{3}

(- 2)^{3} = - 8

= - 8

Prime factorization of

8 : 2^{3}

= - 2^{3}

Apply exponent rule:

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

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

= - 2^{2} \cdot 2

Apply radical rule:

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

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

= 2^{2} - 2

Apply radical rule:

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

2^{2} = 2

= 2 - 2

Apply radical rule:

- a = a - 1

- 2 = 2 - 1

= 22 - 1

Apply imaginary number rule:

- 1 = i

= 22 i

(e^{x} - e^{- x}) (e^{a} - e^{- a})^{- 1}

2^{- x} cos (x)

1.24 \times 1 0^{- 10}

(4.49 x 1 0^{10}) x (1.81 x 1 0^{10})

145.7 \cdot 1 0^{- 6}