Simplify (-2i)^6

${(- 2 i)}^{6}$

Step 1

Apply the product rule to $- 2 i$ .

${(- 2)}^{6} i^{6}$

Step 2

Raise $- 2$ to the power of $6$ .

$64 i^{6}$

Step 3

Factor out $i^{4}$ .

$64 (i^{4} i^{2})$

Step 4

Rewrite $i^{4}$ as $1$ .

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$64 ({(i^{2})}^{2} i^{2})$

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

$64 ({(- 1)}^{2} i^{2})$

Raise $- 1$ to the power of $2$ .

$64 (1 i^{2})$

$64 (1 i^{2})$

Step 5

Multiply $i^{2}$ by $1$ .

$64 i^{2}$

Step 6

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

$64 \cdot - 1$

Step 7

Multiply $64$ by $- 1$ .

$- 64$

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