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Popular >

simplify (sqrt(-5))^3

Solution

simplify

(- 5)^{3}

Solution

- 55 i

Solution steps

(- 5)^{3}

- 5 = 5 i

= (5 i)^{3}

Apply exponent rule:

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

(5 i)^{3} = (5)^{3} i^{3}

= (5)^{3} i^{3}

(5)^{3} = 55

= 55 i^{3}

Simplify

i^{3} : - i

= 55 (- i)

Apply rule:

a (- b) = - ab

55 (- i) = - 55 i

= - 55 i

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Frequently Asked Questions (FAQ)

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