Algebra Examples

$i^{5} \cdot i^{11} \cdot i^{18} \cdot i^{8}$

Step 1

Factor out $i^{4}$ .

$i^{4} i \cdot i^{11} \cdot i^{18} \cdot i^{8}$

Step 2

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

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Step 2.1

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

${(i^{2})}^{2} i \cdot i^{11} \cdot i^{18} \cdot i^{8}$

Step 2.2

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

${(- 1)}^{2} i \cdot i^{11} \cdot i^{18} \cdot i^{8}$

Step 2.3

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

$1 i \cdot i^{11} \cdot i^{18} \cdot i^{8}$

Step 3

Multiply $i$ by $1$ .

$i \cdot i^{11} \cdot i^{18} \cdot i^{8}$

Step 4

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

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Step 4.1

Factor out $i^{8}$ .

$i \cdot (i^{8} i^{3}) \cdot i^{18} \cdot i^{8}$

Step 4.2

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

$i \cdot ({(i^{4})}^{2} i^{3}) \cdot i^{18} \cdot i^{8}$

Step 4.3

Factor out $i^{2}$ .

$i \cdot ({(i^{4})}^{2} (i^{2} \cdot i)) \cdot i^{18} \cdot i^{8}$

Step 5

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

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Step 5.1

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

$i \cdot ({({(i^{2})}^{2})}^{2} (i^{2} \cdot i)) \cdot i^{18} \cdot i^{8}$

Step 5.2

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

$i \cdot ({({(- 1)}^{2})}^{2} (i^{2} \cdot i)) \cdot i^{18} \cdot i^{8}$

Step 5.3

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

$i \cdot (1^{2} (i^{2} \cdot i)) \cdot i^{18} \cdot i^{8}$

Step 6

One to any power is one.

$i \cdot (1 (i^{2} \cdot i)) \cdot i^{18} \cdot i^{8}$

Step 7

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

$i \cdot (i^{2} \cdot i) \cdot i^{18} \cdot i^{8}$

Step 8

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

$i \cdot (- 1 \cdot i) \cdot i^{18} \cdot i^{8}$

Step 9

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

$i \cdot (- i) \cdot i^{18} \cdot i^{8}$

Step 10

Multiply $i (- i)$ .

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Step 10.1

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

$- (i^{1} i) \cdot i^{18} \cdot i^{8}$

Step 10.2

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

$- (i^{1} i^{1}) \cdot i^{18} \cdot i^{8}$

Step 10.3

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

$- i^{1 + 1} \cdot i^{18} \cdot i^{8}$

Step 10.4

Add $1$ and $1$ .

$- i^{2} \cdot i^{18} \cdot i^{8}$

Step 11

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

$- - 1 \cdot i^{18} \cdot i^{8}$

Step 12

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{18} \cdot i^{8}$

Step 13

Multiply $i^{18}$ by $1$ .

$i^{18} \cdot i^{8}$

Step 14

Rewrite $i^{18}$ as ${(i^{4})}^{4} i^{2}$ .

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Step 14.1

Factor out $i^{16}$ .

$i^{16} i^{2} \cdot i^{8}$

Step 14.2

Rewrite $i^{16}$ as ${(i^{4})}^{4}$ .

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

Step 15

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

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Step 15.1

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

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

Step 15.2

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

${({(- 1)}^{2})}^{4} i^{2} \cdot i^{8}$

Step 15.3

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

$1^{4} i^{2} \cdot i^{8}$

Step 16

One to any power is one.

$1 i^{2} \cdot i^{8}$

Step 17

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

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

Step 18

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

$- 1 \cdot i^{8}$

Step 19

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

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

Step 20

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

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Step 20.1

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

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

Step 20.2

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

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

Step 20.3

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

$- 1 \cdot 1^{2}$

Step 21

One to any power is one.

$- 1 \cdot 1$

Step 22

Multiply $- 1$ by $1$ .

$- 1$