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Popular >

simplify (-3i)^3

Solution

simplify

(- 3 i)^{3}

Solution

27 i

Solution steps

(- 3 i)^{3}

Apply exponent rule:

(- a)^{n} = - a^{n},

if

n

is odd

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

= - (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

Popular Examples

8 t - 0.8 t - 10 = 0

factor 6m-9n+21nx-14mx factor

6 m - 9 n + 21 n x - 14 m x

x^{2} + 6 x - 27 \geq 0

solvefor y,y^2=x^3+48662*x^2+x solve for

y, y^{2} = x^{3} + 48662 \cdot x^{2} + x

(5 x - 2)^{2} = 16

Frequently Asked Questions (FAQ)

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