Algebra Examples

$i^{10} \cdot i^{37} \cdot i^{36}$

Step 1

Rewrite $i^{10}$ as ${(i^{4})}^{2} i^{2}$ .

Tap for more steps...

Step 1.1

Factor out $i^{8}$ .

$i^{8} i^{2} \cdot i^{37} \cdot i^{36}$

Step 1.2

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

${(i^{4})}^{2} i^{2} \cdot i^{37} \cdot i^{36}$

${(i^{4})}^{2} i^{2} \cdot i^{37} \cdot i^{36}$

Step 2

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

Tap for more steps...

Step 2.1

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

${({(i^{2})}^{2})}^{2} i^{2} \cdot i^{37} \cdot i^{36}$

Step 2.2

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

${({(- 1)}^{2})}^{2} i^{2} \cdot i^{37} \cdot i^{36}$

Step 2.3

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

$1^{2} i^{2} \cdot i^{37} \cdot i^{36}$

$1^{2} i^{2} \cdot i^{37} \cdot i^{36}$

Step 3

One to any power is one.

$1 i^{2} \cdot i^{37} \cdot i^{36}$

Step 4

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

$i^{2} \cdot i^{37} \cdot i^{36}$

Step 5

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

$- 1 \cdot i^{37} \cdot i^{36}$

Step 6

Rewrite $i^{37}$ as ${(i^{4})}^{9} i$ .

Tap for more steps...

Step 6.1

Factor out $i^{36}$ .

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

Step 6.2

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

$- 1 \cdot ({(i^{4})}^{9} i) \cdot i^{36}$

$- 1 \cdot ({(i^{4})}^{9} i) \cdot i^{36}$

Step 7

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

Tap for more steps...

Step 7.1

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

$- 1 \cdot ({({(i^{2})}^{2})}^{9} i) \cdot i^{36}$

Step 7.2

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

$- 1 \cdot ({({(- 1)}^{2})}^{9} i) \cdot i^{36}$

Step 7.3

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

$- 1 \cdot (1^{9} i) \cdot i^{36}$

$- 1 \cdot (1^{9} i) \cdot i^{36}$

Step 8

One to any power is one.

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

Step 9

Multiply $i$ by $1$ .

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

Step 10

Rewrite $- 1 i$ as $- i$ .

$- i \cdot i^{36}$

Step 11

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

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

Step 12

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

Tap for more steps...

Step 12.1

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

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

Step 12.2

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

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

Step 12.3

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

$- i \cdot 1^{9}$

$- i \cdot 1^{9}$

Step 13

One to any power is one.

$- i \cdot 1$

Step 14

Multiply $- 1$ by $1$ .

$- i$

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