Algebra Examples

i^{33}

$i^{33}$

Step 1

Rewrite

i^{33}

$i^{33}$ as

{(i^{4})}^{8} i

${(i^{4})}^{8} i$ .

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Step 1.1

Factor out

i^{32}

$i^{32}$ .

i^{32} i

$i^{32} i$

Step 1.2

Rewrite

i^{32}

$i^{32}$ as

{(i^{4})}^{8}

${(i^{4})}^{8}$ .

{(i^{4})}^{8} i

${(i^{4})}^{8} i$

{(i^{4})}^{8} i

${(i^{4})}^{8} i$

Step 2

Rewrite

i^{4}

$i^{4}$ as

1

$1$ .

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Step 2.1

Rewrite

i^{4}

$i^{4}$ as

{(i^{2})}^{2}

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

{({(i^{2})}^{2})}^{8} i

${({(i^{2})}^{2})}^{8} i$

Step 2.2

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

{({(- 1)}^{2})}^{8} i

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

Step 2.3

Raise

- 1

$- 1$ to the power of

2

$2$ .

1^{8} i

$1^{8} i$

1^{8} i

$1^{8} i$

Step 3

One to any power is one.

1 i

$1 i$

Step 4

Multiply

i

$i$ by

1

$1$ .

i

$i$

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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