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

The solution to (-2i)^2(3i)^3 is 108i

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simplify (-2i)^2(3i)^3

simplify

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

108 i

Solution steps

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

Simplify

(- 2 i)^{2} : - 4

= - 4 (3 i)^{3}

Apply exponent rule:

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

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

= - 4 \cdot 3^{3} i^{3}

3^{3} = 27

= - 4 \cdot 27 i^{3}

Apply exponent rule:

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

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

= - 4 \cdot 27 i^{2} i

Apply imaginary number rule:

i^{2} = - 1

= - 4 \cdot 27 (- 1 i)

Apply rule:

1 \cdot a = a

- 1 i = - i

= - 4 \cdot 27 (- i)

Apply rule:

a (- b) = - ab

27 (- i) = - 27 i

= - 4 (- 27 i)

Apply rule:

- a (- b) = ab

- 4 (- 27 i) = 4 \cdot 27 i

= 4 \cdot 27 i

Multiply the numbers:

4 \cdot 27 = 108

= 108 i

(b + a)^{2}

(7 x - 1) 2

- (10 n - 9.1 p) - 3.4

3 a + (a + 7 b - 4 c) - (3 a + 5 b - 3 c) - (b - c)

(3 - 52)^{2}