Algebra Examples

i^{22}

$i^{22}$

Step 1

Rewrite

$i^{22}$ as

${(i^{4})}^{5} i^{2}$ .

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Step 1.1

Factor out

$i^{20}$ .

$i^{20} i^{2}$

Step 1.2

Rewrite

$i^{20}$ as

${(i^{4})}^{5}$ .

${(i^{4})}^{5} i^{2}$

${(i^{4})}^{5} i^{2}$

Step 2

Rewrite

$i^{4}$ as

$1$ .

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Step 2.1

Rewrite

$i^{4}$ as

${(i^{2})}^{2}$ .

${({(i^{2})}^{2})}^{5} i^{2}$

Step 2.2

Rewrite

$i^{2}$ as

$- 1$ .

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

Step 2.3

Raise

$- 1$ to the power of

$2$ .

$1^{5} i^{2}$

$1^{5} i^{2}$

Step 3

One to any power is one.

$1 i^{2}$

Step 4

Multiply

$i^{2}$ by

$1$ .

$i^{2}$

Step 5

Rewrite

$i^{2}$ as

$- 1$ .

$- 1$

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