Algebra Examples

$i^{7} \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Step 1

Rewrite $i^{7}$ as $i^{4} (i^{2} \cdot i)$ .

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Step 1.1

Factor out $i^{4}$ .

$i^{4} i^{3} \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Step 1.2

Factor out $i^{2}$ .

$i^{4} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Step 2

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

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Step 2.1

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

${(i^{2})}^{2} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Step 2.2

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

${(- 1)}^{2} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Step 2.3

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

$1 (i^{2} \cdot i) \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Step 3

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

$i^{2} \cdot i \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Step 4

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

$- 1 \cdot i \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Step 5

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

$- i \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Step 6

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

$- i \cdot {(i^{4})}^{7} \cdot i^{25} \cdot i^{19}$

Step 7

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

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Step 7.1

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

$- i \cdot {({(i^{2})}^{2})}^{7} \cdot i^{25} \cdot i^{19}$

Step 7.2

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

$- i \cdot {({(- 1)}^{2})}^{7} \cdot i^{25} \cdot i^{19}$

Step 7.3

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

$- i \cdot 1^{7} \cdot i^{25} \cdot i^{19}$

Step 8

One to any power is one.

$- i \cdot 1 \cdot i^{25} \cdot i^{19}$

Step 9

Multiply $- 1$ by $1$ .

$- i \cdot i^{25} \cdot i^{19}$

Step 10

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

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Step 10.1

Factor out $i^{24}$ .

$- i \cdot (i^{24} i) \cdot i^{19}$

Step 10.2

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

$- i \cdot ({(i^{4})}^{6} i) \cdot i^{19}$

Step 11

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

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Step 11.1

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

$- i \cdot ({({(i^{2})}^{2})}^{6} i) \cdot i^{19}$

Step 11.2

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

$- i \cdot ({({(- 1)}^{2})}^{6} i) \cdot i^{19}$

Step 11.3

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

$- i \cdot (1^{6} i) \cdot i^{19}$

Step 12

One to any power is one.

$- i \cdot (1 i) \cdot i^{19}$

Step 13

Multiply $i$ by $1$ .

$- i \cdot i \cdot i^{19}$

Step 14

Multiply $- i i$ .

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Step 14.1

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

$- (i^{1} i) \cdot i^{19}$

Step 14.2

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

$- (i^{1} i^{1}) \cdot i^{19}$

Step 14.3

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

$- i^{1 + 1} \cdot i^{19}$

Step 14.4

Add $1$ and $1$ .

$- i^{2} \cdot i^{19}$

Step 15

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

$- - 1 \cdot i^{19}$

Step 16

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{19}$

Step 17

Multiply $i^{19}$ by $1$ .

$i^{19}$

Step 18

Rewrite $i^{19}$ as ${(i^{4})}^{4} (i^{2} \cdot i)$ .

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Step 18.1

Factor out $i^{16}$ .

$i^{16} i^{3}$

Step 18.2

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

${(i^{4})}^{4} i^{3}$

Step 18.3

Factor out $i^{2}$ .

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

Step 19

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

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Step 19.1

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

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

Step 19.2

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

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

Step 19.3

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

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

Step 20

One to any power is one.

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

Step 21

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

$i^{2} \cdot i$

Step 22

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

$- 1 \cdot i$

Step 23

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

$- i$