Basic Math Examples

$i^{12} - i^{14}$

Step 1

Simplify each term.

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Step 1.1

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

${(i^{4})}^{3} - i^{14}$

Step 1.2

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

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Step 1.2.1

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

${({(i^{2})}^{2})}^{3} - i^{14}$

Step 1.2.2

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

${({(- 1)}^{2})}^{3} - i^{14}$

Step 1.2.3

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

$1^{3} - i^{14}$

$1^{3} - i^{14}$

Step 1.3

One to any power is one.

$1 - i^{14}$

Step 1.4

Rewrite $i^{14}$ as ${(i^{4})}^{3} i^{2}$ .

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Step 1.4.1

Factor out $i^{12}$ .

$1 - (i^{12} i^{2})$

Step 1.4.2

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

$1 - ({(i^{4})}^{3} i^{2})$

$1 - ({(i^{4})}^{3} i^{2})$

Step 1.5

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

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Step 1.5.1

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

$1 - ({({(i^{2})}^{2})}^{3} i^{2})$

Step 1.5.2

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

$1 - ({({(- 1)}^{2})}^{3} i^{2})$

Step 1.5.3

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

$1 - (1^{3} i^{2})$

$1 - (1^{3} i^{2})$

Step 1.6

One to any power is one.

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

Step 1.7

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

$1 - i^{2}$

Step 1.8

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

$1 - - 1$

Step 1.9

Multiply $- 1$ by $- 1$ .

$1 + 1$

$1 + 1$

Step 2

Add $1$ and $1$ .

$2$

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