Basic Math Examples

$5 - i^{8} + 2 i^{32}$

Step 1

Simplify each term.

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Step 1.1

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

$5 - {(i^{4})}^{2} + 2 i^{32}$

Step 1.2

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

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Step 1.2.1

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

$5 - {({(i^{2})}^{2})}^{2} + 2 i^{32}$

Step 1.2.2

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

$5 - {({(- 1)}^{2})}^{2} + 2 i^{32}$

Step 1.2.3

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

$5 - 1^{2} + 2 i^{32}$

$5 - 1^{2} + 2 i^{32}$

Step 1.3

One to any power is one.

$5 - 1 \cdot 1 + 2 i^{32}$

Step 1.4

Multiply $- 1$ by $1$ .

$5 - 1 + 2 i^{32}$

Step 1.5

Rewrite $i^{32}$ as ${(i^{4})}^{8}$ .

$5 - 1 + 2 {(i^{4})}^{8}$

Step 1.6

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

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Step 1.6.1

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

$5 - 1 + 2 {({(i^{2})}^{2})}^{8}$

Step 1.6.2

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

$5 - 1 + 2 {({(- 1)}^{2})}^{8}$

Step 1.6.3

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

$5 - 1 + 2 \cdot 1^{8}$

$5 - 1 + 2 \cdot 1^{8}$

Step 1.7

One to any power is one.

$5 - 1 + 2 \cdot 1$

Step 1.8

Multiply $2$ by $1$ .

$5 - 1 + 2$

$5 - 1 + 2$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Subtract $1$ from $5$ .

$4 + 2$

Step 2.2

Add $4$ and $2$ .

$6$

$6$

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