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Popular >

simplify (sqrt(-4))^3

Solution

simplify

(- 4)^{3}

Solution

- 8 i

Solution steps

(- 4)^{3}

- 4 = 2 i

= (2 i)^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 i)^{3} = 2^{3} i^{3}

= 2^{3} i^{3}

2^{3} = 8

= 8 i^{3}

Apply exponent rule:

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

i^{3} = i^{2} i

= 8 i^{2} i

Apply imaginary number rule:

i^{2} = - 1

= 8 (- 1 i)

Apply rule:

1 \cdot a = a

- 1 i = - i

= 8 (- i)

Apply rule:

a (- b) = - ab

8 (- i) = - 8 i

= - 8 i

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Frequently Asked Questions (FAQ)

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