Precalculus Examples

$i^{9} + i^{- 5}$

Step 1

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

Tap for more steps...

Step 1.1

Factor out $i^{8}$ .

$i^{8} i + i^{- 5}$

Step 1.2

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

${(i^{4})}^{2} i + i^{- 5}$

${(i^{4})}^{2} i + i^{- 5}$

Step 2

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

Tap for more steps...

Step 2.1

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

${({(i^{2})}^{2})}^{2} i + i^{- 5}$

Step 2.2

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

${({(- 1)}^{2})}^{2} i + i^{- 5}$

Step 2.3

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

$1^{2} i + i^{- 5}$

$1^{2} i + i^{- 5}$

Step 3

One to any power is one.

$1 i + i^{- 5}$

Step 4

Multiply $i$ by $1$ .

$i + i^{- 5}$

Step 5

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

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

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

Factor out $i^{4}$ .

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

Step 6.2

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

Tap for more steps...

Step 6.2.1

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

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

Step 6.2.2

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

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

Step 6.2.3

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

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

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

Step 6.3

Multiply $i$ by $1$ .

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$