Algebra Examples

$i^{8} \cdot i^{15} \cdot i^{28} \cdot i^{25}$

Step 1

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

${(i^{4})}^{2} \cdot i^{15} \cdot i^{28} \cdot i^{25}$

Step 2

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

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Step 2.1

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

${({(i^{2})}^{2})}^{2} \cdot i^{15} \cdot i^{28} \cdot i^{25}$

Step 2.2

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

${({(- 1)}^{2})}^{2} \cdot i^{15} \cdot i^{28} \cdot i^{25}$

Step 2.3

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

$1^{2} \cdot i^{15} \cdot i^{28} \cdot i^{25}$

Step 3

One to any power is one.

$1 \cdot i^{15} \cdot i^{28} \cdot i^{25}$

Step 4

Multiply $i^{15}$ by $1$ .

$i^{15} \cdot i^{28} \cdot i^{25}$

Step 5

Rewrite $i^{15}$ as ${(i^{4})}^{3} (i^{2} \cdot i)$ .

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Step 5.1

Factor out $i^{12}$ .

$i^{12} i^{3} \cdot i^{28} \cdot i^{25}$

Step 5.2

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

${(i^{4})}^{3} i^{3} \cdot i^{28} \cdot i^{25}$

Step 5.3

Factor out $i^{2}$ .

${(i^{4})}^{3} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25}$

Step 6

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

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Step 6.1

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

${({(i^{2})}^{2})}^{3} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25}$

Step 6.2

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

${({(- 1)}^{2})}^{3} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25}$

Step 6.3

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

$1^{3} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25}$

Step 7

One to any power is one.

$1 (i^{2} \cdot i) \cdot i^{28} \cdot i^{25}$

Step 8

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

$i^{2} \cdot i \cdot i^{28} \cdot i^{25}$

Step 9

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

$- 1 \cdot i \cdot i^{28} \cdot i^{25}$

Step 10

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

$- i \cdot i^{28} \cdot i^{25}$

Step 11

Rewrite $i^{28}$ as ${(i^{4})}^{7}$ .

$- i \cdot {(i^{4})}^{7} \cdot i^{25}$

Step 12

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

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Step 12.1

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

$- i \cdot {({(i^{2})}^{2})}^{7} \cdot i^{25}$

Step 12.2

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

$- i \cdot {({(- 1)}^{2})}^{7} \cdot i^{25}$

Step 12.3

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

$- i \cdot 1^{7} \cdot i^{25}$

Step 13

One to any power is one.

$- i \cdot 1 \cdot i^{25}$

Step 14

Multiply $- 1$ by $1$ .

$- i \cdot i^{25}$

Step 15

Rewrite $i^{25}$ as ${(i^{4})}^{6} i$ .

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Step 15.1

Factor out $i^{24}$ .

$- i \cdot (i^{24} i)$

Step 15.2

Rewrite $i^{24}$ as ${(i^{4})}^{6}$ .

$- i \cdot ({(i^{4})}^{6} i)$

Step 16

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

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Step 16.1

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

$- i \cdot ({({(i^{2})}^{2})}^{6} i)$

Step 16.2

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

$- i \cdot ({({(- 1)}^{2})}^{6} i)$

Step 16.3

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

$- i \cdot (1^{6} i)$

Step 17

One to any power is one.

$- i \cdot (1 i)$

Step 18

Multiply $i$ by $1$ .

$- i \cdot i$

Step 19

Multiply $- i i$ .

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Step 19.1

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

$- (i^{1} i)$

Step 19.2

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

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

Step 19.3

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

$- i^{1 + 1}$

Step 19.4

Add $1$ and $1$ .

$- i^{2}$

Step 20

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

$- - 1$

Step 21

Multiply $- 1$ by $- 1$ .

$1$