Algebra Examples

$i^{3} \cdot i^{7}$

Step 1

Factor out $i^{2}$ .

$i^{2} \cdot i \cdot i^{7}$

Step 2

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

$- 1 \cdot i \cdot i^{7}$

Step 3

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

$- i \cdot i^{7}$

Step 4

Rewrite $i^{7}$ as $i^{4} (i^{2} \cdot i)$ .

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Step 4.1

Factor out $i^{4}$ .

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

Step 4.2

Factor out $i^{2}$ .

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

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

Step 6

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

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

Step 7

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

$- i \cdot (- 1 \cdot i)$

Step 8

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

$- i \cdot (- i)$

Step 9

Multiply $- i (- i)$ .

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Step 9.1

Multiply $- 1$ by $- 1$ .

$1 i i$

Step 9.2

Raise $i$ to the power of $1$ .

$1 (i^{1} i)$

Step 9.3

Raise $i$ to the power of $1$ .

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

Step 9.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1 i^{1 + 1}$

Step 9.5

Add $1$ and $1$ .

$1 i^{2}$

Step 9.6

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

$i^{2}$

$i^{2}$

Step 10

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

$- 1$

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