Algebra Examples

$i^{10} \cdot i^{11} \cdot i^{20}$

Step 1

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

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Step 1.1

Factor out $i^{8}$ .

$i^{8} i^{2} \cdot i^{11} \cdot i^{20}$

Step 1.2

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

${(i^{4})}^{2} i^{2} \cdot i^{11} \cdot i^{20}$

Step 2

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

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Step 2.1

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

${({(i^{2})}^{2})}^{2} i^{2} \cdot i^{11} \cdot i^{20}$

Step 2.2

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

${({(- 1)}^{2})}^{2} i^{2} \cdot i^{11} \cdot i^{20}$

Step 2.3

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

$1^{2} i^{2} \cdot i^{11} \cdot i^{20}$

Step 3

One to any power is one.

$1 i^{2} \cdot i^{11} \cdot i^{20}$

Step 4

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

$i^{2} \cdot i^{11} \cdot i^{20}$

Step 5

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

$- 1 \cdot i^{11} \cdot i^{20}$

Step 6

Rewrite $i^{11}$ as ${(i^{4})}^{2} (i^{2} \cdot i)$ .

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Step 6.1

Factor out $i^{8}$ .

$- 1 \cdot (i^{8} i^{3}) \cdot i^{20}$

Step 6.2

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

$- 1 \cdot ({(i^{4})}^{2} i^{3}) \cdot i^{20}$

Step 6.3

Factor out $i^{2}$ .

$- 1 \cdot ({(i^{4})}^{2} (i^{2} \cdot i)) \cdot i^{20}$

Step 7

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

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Step 7.1

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

$- 1 \cdot ({({(i^{2})}^{2})}^{2} (i^{2} \cdot i)) \cdot i^{20}$

Step 7.2

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

$- 1 \cdot ({({(- 1)}^{2})}^{2} (i^{2} \cdot i)) \cdot i^{20}$

Step 7.3

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

$- 1 \cdot (1^{2} (i^{2} \cdot i)) \cdot i^{20}$

Step 8

One to any power is one.

$- 1 \cdot (1 (i^{2} \cdot i)) \cdot i^{20}$

Step 9

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

$- 1 \cdot (i^{2} \cdot i) \cdot i^{20}$

Step 10

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

$- 1 \cdot (- 1 \cdot i) \cdot i^{20}$

Step 11

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

$- 1 \cdot (- i) \cdot i^{20}$

Step 12

Multiply $- 1$ by $- 1$ .

$1 i \cdot i^{20}$

Step 13

Multiply $i$ by $1$ .

$i \cdot i^{20}$

Step 14

Rewrite $i^{20}$ as ${(i^{4})}^{5}$ .

$i \cdot {(i^{4})}^{5}$

Step 15

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

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Step 15.1

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

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

Step 15.2

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

$i \cdot {({(- 1)}^{2})}^{5}$

Step 15.3

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

$i \cdot 1^{5}$

Step 16

One to any power is one.

$i \cdot 1$

Step 17

Multiply $i$ by $1$ .

$i$