Simplify the Radical Expression (-4i)^3*2i

${(- 4 i)}^{3} \cdot 2 i$

Step 1

Apply the product rule to $- 4 i$ .

${(- 4)}^{3} i^{3} \cdot 2 i$

Step 2

Raise $- 4$ to the power of $3$ .

$- 64 i^{3} \cdot 2 i$

Step 3

Factor out $i^{2}$ .

$- 64 (i^{2} \cdot i) \cdot 2 i$

Step 4

Rewrite $i^{2}$ as $- 1$ .

$- 64 (- 1 \cdot i) \cdot 2 i$

Step 5

Rewrite $- 1 i$ as $- i$ .

$- 64 (- i) \cdot 2 i$

Step 6

Multiply $- 1$ by $- 64$ .

$64 i \cdot 2 i$

Step 7

Multiply $2$ by $64$ .

$128 i i$

Step 8

Multiply $128 i i$ .

Raise $i$ to the power of $1$ .

$128 (i^{1} i)$

Raise $i$ to the power of $1$ .

$128 (i^{1} i^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$128 i^{1 + 1}$

Add $1$ and $1$ .

$128 i^{2}$

Step 9

Rewrite $i^{2}$ as $- 1$ .

$128 \cdot - 1$

Step 10

Multiply $128$ by $- 1$ .

$- 128$