Simplify i^-6

$i^{- 6}$

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

$\frac{1}{i^{6}}$

Simplify the denominator.

Factor out $i^{4}$ .

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

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

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

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

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

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

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

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

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

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

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

$\frac{1}{- 1}$

Divide $1$ by $- 1$ .

$- 1$