Simplify i^-9

$i^{- 9}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{i^{9}}$

Step 2

Simplify the denominator.

Rewrite $i^{9}$ as ${(i^{4})}^{2} i$ .

Factor out $i^{8}$ .

$\frac{1}{i^{8} i}$

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

$\frac{1}{{(i^{4})}^{2} i}$

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

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

$\frac{1}{{({(i^{2})}^{2})}^{2} i}$

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

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

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

$\frac{1}{1^{2} i}$

One to any power is one.

$\frac{1}{1 i}$

Multiply $i$ by $1$ .

$\frac{1}{i}$