Simplify 1/(i^-10)

$\frac{1}{i^{- 10}}$

Step 1

Move $i^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$i^{10}$

Step 2

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

Factor out $i^{8}$ .

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

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

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

Step 3

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 $2$ .

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

Step 4

One to any power is one.

$1 i^{2}$

Step 5

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

$i^{2}$

Step 6

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

$- 1$