Basic Math Examples

$2 i^{15} - i^{7}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{15}$ as ${(i^{4})}^{3} (i^{2} \cdot i)$ .

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Step 1.1.1

Factor out $i^{12}$ .

$2 (i^{12} i^{3}) - i^{7}$

Step 1.1.2

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

$2 ({(i^{4})}^{3} i^{3}) - i^{7}$

Step 1.1.3

Factor out $i^{2}$ .

$2 ({(i^{4})}^{3} (i^{2} \cdot i)) - i^{7}$

$2 ({(i^{4})}^{3} (i^{2} \cdot i)) - i^{7}$

Step 1.2

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

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Step 1.2.1

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

$2 ({({(i^{2})}^{2})}^{3} (i^{2} \cdot i)) - i^{7}$

Step 1.2.2

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

$2 ({({(- 1)}^{2})}^{3} (i^{2} \cdot i)) - i^{7}$

Step 1.2.3

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

$2 (1^{3} (i^{2} \cdot i)) - i^{7}$

$2 (1^{3} (i^{2} \cdot i)) - i^{7}$

Step 1.3

One to any power is one.

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

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

Step 1.7

Multiply $- 1$ by $2$ .

$- 2 i - i^{7}$

Step 1.8

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

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Step 1.8.1

Factor out $i^{4}$ .

$- 2 i - (i^{4} i^{3})$

Step 1.8.2

Factor out $i^{2}$ .

$- 2 i - (i^{4} (i^{2} \cdot i))$

$- 2 i - (i^{4} (i^{2} \cdot i))$

Step 1.9

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

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Step 1.9.1

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

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

Step 1.9.2

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

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

Step 1.9.3

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

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

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

Step 1.10

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

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

Step 1.11

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

$- 2 i - (- 1 \cdot i)$

Step 1.12

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

$- 2 i - - i$

Step 1.13

Multiply $- 1$ by $- 1$ .

$- 2 i + 1 i$

Step 1.14

Multiply $i$ by $1$ .

$- 2 i + i$

$- 2 i + i$

Step 2

Add $- 2 i$ and $i$ .

$- i$

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