Algebra Examples

$i^{5} \cdot i^{36} \cdot i^{29}$

Step 1

Factor out $i^{4}$ .

$i^{4} i \cdot i^{36} \cdot i^{29}$

Step 2

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

Tap for more steps...

Step 2.1

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

${(i^{2})}^{2} i \cdot i^{36} \cdot i^{29}$

Step 2.2

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

${(- 1)}^{2} i \cdot i^{36} \cdot i^{29}$

Step 2.3

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

$1 i \cdot i^{36} \cdot i^{29}$

$1 i \cdot i^{36} \cdot i^{29}$

Step 3

Multiply $i$ by $1$ .

$i \cdot i^{36} \cdot i^{29}$

Step 4

Rewrite $i^{36}$ as ${(i^{4})}^{9}$ .

$i \cdot {(i^{4})}^{9} \cdot i^{29}$

Step 5

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

Tap for more steps...

Step 5.1

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

$i \cdot {({(i^{2})}^{2})}^{9} \cdot i^{29}$

Step 5.2

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

$i \cdot {({(- 1)}^{2})}^{9} \cdot i^{29}$

Step 5.3

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

$i \cdot 1^{9} \cdot i^{29}$

$i \cdot 1^{9} \cdot i^{29}$

Step 6

One to any power is one.

$i \cdot 1 \cdot i^{29}$

Step 7

Multiply $i$ by $1$ .

$i \cdot i^{29}$

Step 8

Rewrite $i^{29}$ as ${(i^{4})}^{7} i$ .

Tap for more steps...

Step 8.1

Factor out $i^{28}$ .

$i \cdot (i^{28} i)$

Step 8.2

Rewrite $i^{28}$ as ${(i^{4})}^{7}$ .

$i \cdot ({(i^{4})}^{7} i)$

$i \cdot ({(i^{4})}^{7} i)$

Step 9

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

Tap for more steps...

Step 9.1

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

$i \cdot ({({(i^{2})}^{2})}^{7} i)$

Step 9.2

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

$i \cdot ({({(- 1)}^{2})}^{7} i)$

Step 9.3

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

$i \cdot (1^{7} i)$

$i \cdot (1^{7} i)$

Step 10

One to any power is one.

$i \cdot (1 i)$

Step 11

Multiply $i$ by $1$ .

$i \cdot i$

Step 12

Multiply $i i$ .

Tap for more steps...

Step 12.1

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

$i^{1} i$

Step 12.2

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

$i^{1} i^{1}$

Step 12.3

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

$i^{1 + 1}$

Step 12.4

Add $1$ and $1$ .

$i^{2}$

$i^{2}$

Step 13

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

$- 1$

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