Simplify (-i)^10

${(- i)}^{10}$

Step 1

Apply the product rule to $- i$ .

${(- 1)}^{10} i^{10}$

Step 2

Raise $- 1$ to the power of $10$ .

$1 i^{10}$

Step 3

Multiply $i^{10}$ by $1$ .

$i^{10}$

Step 4

Rewrite $i^{10}$ as ${(i^{4})}^{2} i^{2}$ .

Factor out $i^{8}$ .

$i^{8} i^{2}$

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

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

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

Step 5

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

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

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

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

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

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

$1^{2} i^{2}$

$1^{2} i^{2}$

Step 6

One to any power is one.

$1 i^{2}$

Step 7

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

$i^{2}$

Step 8

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

$- 1$

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