Algebra Examples

$i^{8} - i^{9} + i^{10}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

${(i^{4})}^{2} - i^{9} + i^{10}$

Step 1.2

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

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Step 1.2.1

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

${({(i^{2})}^{2})}^{2} - i^{9} + i^{10}$

Step 1.2.2

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

${({(- 1)}^{2})}^{2} - i^{9} + i^{10}$

Step 1.2.3

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

$1^{2} - i^{9} + i^{10}$

$1^{2} - i^{9} + i^{10}$

Step 1.3

One to any power is one.

$1 - i^{9} + i^{10}$

Step 1.4

Rewrite $i^{9}$ as ${(i^{4})}^{2} i$ .

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Step 1.4.1

Factor out $i^{8}$ .

$1 - (i^{8} i) + i^{10}$

Step 1.4.2

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

$1 - ({(i^{4})}^{2} i) + i^{10}$

$1 - ({(i^{4})}^{2} i) + i^{10}$

Step 1.5

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

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Step 1.5.1

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

$1 - ({({(i^{2})}^{2})}^{2} i) + i^{10}$

Step 1.5.2

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

$1 - ({({(- 1)}^{2})}^{2} i) + i^{10}$

Step 1.5.3

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

$1 - (1^{2} i) + i^{10}$

$1 - (1^{2} i) + i^{10}$

Step 1.6

One to any power is one.

$1 - (1 i) + i^{10}$

Step 1.7

Multiply $i$ by $1$ .

$1 - i + i^{10}$

Step 1.8

Rewrite $i^{10}$ as ${(i^{4})}^{2} i^{2}$ .

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Step 1.8.1

Factor out $i^{8}$ .

$1 - i + i^{8} i^{2}$

Step 1.8.2

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

$1 - i + {(i^{4})}^{2} i^{2}$

$1 - i + {(i^{4})}^{2} i^{2}$

Step 1.9

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

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Step 1.9.1

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

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

Step 1.9.2

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

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

Step 1.9.3

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

$1 - i + 1^{2} i^{2}$

$1 - i + 1^{2} i^{2}$

Step 1.10

One to any power is one.

$1 - i + 1 i^{2}$

Step 1.11

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

$1 - i + i^{2}$

Step 1.12

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

$1 - i - 1$

$1 - i - 1$

Step 2

Simplify by subtracting numbers.

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Step 2.1

Subtract $1$ from $1$ .

$0 - i$

Step 2.2

Subtract $i$ from $0$ .

$- i$

$- i$

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