Algebra Examples

$i^{8} \cdot i^{31} \cdot i^{28}$

Step 1

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

${(i^{4})}^{2} \cdot i^{31} \cdot i^{28}$

Step 2

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

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Step 2.1

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

${({(i^{2})}^{2})}^{2} \cdot i^{31} \cdot i^{28}$

Step 2.2

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

${({(- 1)}^{2})}^{2} \cdot i^{31} \cdot i^{28}$

Step 2.3

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

$1^{2} \cdot i^{31} \cdot i^{28}$

$1^{2} \cdot i^{31} \cdot i^{28}$

Step 3

One to any power is one.

$1 \cdot i^{31} \cdot i^{28}$

Step 4

Multiply $i^{31}$ by $1$ .

$i^{31} \cdot i^{28}$

Step 5

Rewrite $i^{31}$ as ${(i^{4})}^{7} (i^{2} \cdot i)$ .

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Step 5.1

Factor out $i^{28}$ .

$i^{28} i^{3} \cdot i^{28}$

Step 5.2

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

${(i^{4})}^{7} i^{3} \cdot i^{28}$

Step 5.3

Factor out $i^{2}$ .

${(i^{4})}^{7} (i^{2} \cdot i) \cdot i^{28}$

${(i^{4})}^{7} (i^{2} \cdot i) \cdot i^{28}$

Step 6

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

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Step 6.1

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

${({(i^{2})}^{2})}^{7} (i^{2} \cdot i) \cdot i^{28}$

Step 6.2

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

${({(- 1)}^{2})}^{7} (i^{2} \cdot i) \cdot i^{28}$

Step 6.3

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

$1^{7} (i^{2} \cdot i) \cdot i^{28}$

$1^{7} (i^{2} \cdot i) \cdot i^{28}$

Step 7

One to any power is one.

$1 (i^{2} \cdot i) \cdot i^{28}$

Step 8

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

$i^{2} \cdot i \cdot i^{28}$

Step 9

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

$- 1 \cdot i \cdot i^{28}$

Step 10

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

$- i \cdot i^{28}$

Step 11

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

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

Step 12

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

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Step 12.1

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

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

Step 12.2

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

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

Step 12.3

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

$- i \cdot 1^{7}$

$- i \cdot 1^{7}$

Step 13

One to any power is one.

$- i \cdot 1$

Step 14

Multiply $- 1$ by $1$ .

$- i$

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