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Popular >

simplify (sqrt((-9)))^3

Solution

simplify

((- 9))^{3}

Solution

- 27 i

Solution steps

(- 9)^{3}

Apply rule:

(- a) = - a

(- 9) = - 9

= (- 9)^{3}

- 9 = 3 i

= (3 i)^{3}

Apply exponent rule:

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

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

= 3^{3} i^{3}

3^{3} = 27

= 27 i^{3}

Apply exponent rule:

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

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

= 27 i^{2} i

Apply imaginary number rule:

i^{2} = - 1

= 27 (- 1 i)

Apply rule:

1 \cdot a = a

- 1 i = - i

= 27 (- i)

Apply rule:

a (- b) = - ab

27 (- i) = - 27 i

= - 27 i

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Frequently Asked Questions (FAQ)

What is (sqrt((-9)))^3 ?
The solution to (sqrt((-9)))^3 is -27i