Simplify i^-46

$i^{- 46}$

Step 1

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

$\frac{1}{i^{46}}$

Step 2

Simplify the denominator.

Rewrite $i^{46}$ as ${(i^{4})}^{11} i^{2}$ .

Factor out $i^{44}$ .

$\frac{1}{i^{44} i^{2}}$

Rewrite $i^{44}$ as ${(i^{4})}^{11}$ .

$\frac{1}{{(i^{4})}^{11} i^{2}}$

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

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

$\frac{1}{{({(i^{2})}^{2})}^{11} i^{2}}$

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

$\frac{1}{{({(- 1)}^{2})}^{11} i^{2}}$

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

$\frac{1}{1^{11} i^{2}}$

One to any power is one.

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

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

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

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

$\frac{1}{- 1}$

Step 3

Divide $1$ by $- 1$ .

$- 1$