Algebra Examples

${(i^{5} \cdot i^{2} \cdot i^{8})}^{0}$

Step 1

Factor out $i^{4}$ .

${(i^{4} i \cdot i^{2} \cdot i^{8})}^{0}$

Step 2

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

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Step 2.1

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

${({(i^{2})}^{2} i \cdot i^{2} \cdot i^{8})}^{0}$

Step 2.2

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

${({(- 1)}^{2} i \cdot i^{2} \cdot i^{8})}^{0}$

Step 2.3

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

${(1 i \cdot i^{2} \cdot i^{8})}^{0}$

${(1 i \cdot i^{2} \cdot i^{8})}^{0}$

Step 3

Multiply $i$ by $1$ .

${(i \cdot i^{2} \cdot i^{8})}^{0}$

Step 4

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

${(i \cdot - 1 \cdot i^{8})}^{0}$

Step 5

Move $- 1$ to the left of $i$ .

${(- 1 \cdot i \cdot i^{8})}^{0}$

Step 6

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

${(- i \cdot i^{8})}^{0}$

Step 7

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

${(- i \cdot {(i^{4})}^{2})}^{0}$

Step 8

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

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Step 8.1

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

${(- i \cdot {({(i^{2})}^{2})}^{2})}^{0}$

Step 8.2

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

${(- i \cdot {({(- 1)}^{2})}^{2})}^{0}$

Step 8.3

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

${(- i \cdot 1^{2})}^{0}$

${(- i \cdot 1^{2})}^{0}$

Step 9

One to any power is one.

${(- i \cdot 1)}^{0}$

Step 10

Multiply $- 1$ by $1$ .

${(- i)}^{0}$

Step 11

Apply the product rule to $- i$ .

${(- 1)}^{0} i^{0}$

Step 12

Anything raised to $0$ is $1$ .

$1 i^{0}$

Step 13

Multiply $i^{0}$ by $1$ .

$i^{0}$

Step 14

Anything raised to $0$ is $1$ .

$1$

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