Simplify (-i)^6

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

Step 1

Apply the product rule to $- i$ .

${(- 1)}^{6} i^{6}$

Step 2

Raise $- 1$ to the power of $6$ .

$1 i^{6}$

Step 3

Multiply $i^{6}$ by $1$ .

$i^{6}$

Step 4

Factor out $i^{4}$ .

$i^{4} i^{2}$

Step 5

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

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

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

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

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

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

$1 i^{2}$

$1 i^{2}$

Step 6

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

$i^{2}$

Step 7

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

$- 1$

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