Algebra Examples

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

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Factor out $i^{4}$ .

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

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

$\frac{1}{1 i}$

Step 1.3

Multiply $i$ by $1$ .

$\frac{1}{i}$

Step 2

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

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

Step 3

Multiply.

Tap for more steps...

Step 3.1

Combine.

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

Step 3.2

Multiply $i$ by $1$ .

$\frac{i}{i i}$

Step 3.3

Simplify the denominator.

Tap for more steps...

Step 3.3.1

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

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

Step 3.3.2

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

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

Step 3.3.3

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

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

Step 3.3.4

Add $1$ and $1$ .

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

Step 3.3.5

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

$\frac{i}{- 1}$

Step 4

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

$- 1 \cdot i$

Step 5

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

$- i$