Finite Math Examples

$- i^{27}$

Step 1

Rewrite $i^{27}$ as ${(i^{4})}^{6} (i^{2} \cdot i)$ .

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Step 1.1

Factor out $i^{24}$ .

$- (i^{24} i^{3})$

Step 1.2

Rewrite $i^{24}$ as ${(i^{4})}^{6}$ .

$- ({(i^{4})}^{6} i^{3})$

Step 1.3

Factor out $i^{2}$ .

$- ({(i^{4})}^{6} (i^{2} \cdot i))$

$- ({(i^{4})}^{6} (i^{2} \cdot i))$

Step 2

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

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Step 2.1

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

$- ({({(i^{2})}^{2})}^{6} (i^{2} \cdot i))$

Step 2.2

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

$- ({({(- 1)}^{2})}^{6} (i^{2} \cdot i))$

Step 2.3

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

$- (1^{6} (i^{2} \cdot i))$

$- (1^{6} (i^{2} \cdot i))$

Step 3

One to any power is one.

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

Step 4

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

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

Step 5

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

$- (- 1 \cdot i)$

Step 6

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

$- - i$

Step 7

Multiply $- 1$ by $- 1$ .

$1 i$

Step 8

Multiply $i$ by $1$ .

$i$

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