Algebra Examples

i^{15}

$i^{15}$

Step 1

Rewrite

i^{15}

$i^{15}$ as

{(i^{4})}^{3} (i^{2} \cdot i)

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

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Step 1.1

Factor out

i^{12}

$i^{12}$ .

i^{12} i^{3}

$i^{12} i^{3}$

Step 1.2

Rewrite

i^{12}

$i^{12}$ as

{(i^{4})}^{3}

${(i^{4})}^{3}$ .

{(i^{4})}^{3} i^{3}

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

Step 1.3

Factor out

i^{2}

$i^{2}$ .

{(i^{4})}^{3} (i^{2} \cdot i)

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

{(i^{4})}^{3} (i^{2} \cdot i)

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

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})}^{3} (i^{2} \cdot i)

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

Step 2.2

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

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

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

Step 2.3

Raise

- 1

$- 1$ to the power of

2

$2$ .

1^{3} (i^{2} \cdot i)

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

1^{3} (i^{2} \cdot i)

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

Step 3

One to any power is one.

1 (i^{2} \cdot i)

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

Step 4

Multiply

i^{2} \cdot i

$i^{2} \cdot i$ by

1

$1$ .

i^{2} \cdot i

$i^{2} \cdot i$

Step 5

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

- 1 \cdot i

$- 1 \cdot i$

Step 6

Rewrite

- 1 i

$- 1 i$ as

- i

$- i$ .

- i

$- i$

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

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