Evaluate i^-5

$i^{- 5}$

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

$\frac{1}{i^{5}}$

Simplify the denominator.

Factor out $i^{4}$ .

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

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

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

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

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

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

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

$\frac{1}{1 i}$

Multiply $i$ by $1$ .

$\frac{1}{i}$

Multiply the numerator and denominator of $\frac{1}{i}$ by the conjugate of $i$ to make the denominator real.

$\frac{1}{i} \cdot \frac{i}{i}$

Multiply.

Combine.

$\frac{1 i}{i i}$

Multiply $i$ by $1$ .

$\frac{i}{i i}$

Simplify the denominator.

Raise $i$ to the power of $1$ .

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

Raise $i$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

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

$\frac{i}{- 1}$

Move the negative one from the denominator of $\frac{i}{- 1}$ .

$- 1 \cdot i$

Rewrite $- 1 \cdot i$ as $- i$ .

$- i$