Algebra Examples

$i^{29} \cdot i^{27} \cdot i^{30}$

Step 1

Rewrite $i^{29}$ as ${(i^{4})}^{7} i$ .

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Step 1.1

Factor out $i^{28}$ .

$i^{28} i \cdot i^{27} \cdot i^{30}$

Step 1.2

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

${(i^{4})}^{7} i \cdot i^{27} \cdot i^{30}$

Step 2

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

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Step 2.1

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

${({(i^{2})}^{2})}^{7} i \cdot i^{27} \cdot i^{30}$

Step 2.2

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

${({(- 1)}^{2})}^{7} i \cdot i^{27} \cdot i^{30}$

Step 2.3

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

$1^{7} i \cdot i^{27} \cdot i^{30}$

Step 3

One to any power is one.

$1 i \cdot i^{27} \cdot i^{30}$

Step 4

Multiply $i$ by $1$ .

$i \cdot i^{27} \cdot i^{30}$

Step 5

Rewrite $i^{27}$ as ${(i^{4})}^{6} (i^{2} \cdot i)$ .

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Step 5.1

Factor out $i^{24}$ .

$i \cdot (i^{24} i^{3}) \cdot i^{30}$

Step 5.2

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

$i \cdot ({(i^{4})}^{6} i^{3}) \cdot i^{30}$

Step 5.3

Factor out $i^{2}$ .

$i \cdot ({(i^{4})}^{6} (i^{2} \cdot i)) \cdot i^{30}$

Step 6

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

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Step 6.1

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

$i \cdot ({({(i^{2})}^{2})}^{6} (i^{2} \cdot i)) \cdot i^{30}$

Step 6.2

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

$i \cdot ({({(- 1)}^{2})}^{6} (i^{2} \cdot i)) \cdot i^{30}$

Step 6.3

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

$i \cdot (1^{6} (i^{2} \cdot i)) \cdot i^{30}$

Step 7

One to any power is one.

$i \cdot (1 (i^{2} \cdot i)) \cdot i^{30}$

Step 8

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

$i \cdot (i^{2} \cdot i) \cdot i^{30}$

Step 9

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

$i \cdot (- 1 \cdot i) \cdot i^{30}$

Step 10

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

$i \cdot (- i) \cdot i^{30}$

Step 11

Multiply $i (- i)$ .

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Step 11.1

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

$- (i^{1} i) \cdot i^{30}$

Step 11.2

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

$- (i^{1} i^{1}) \cdot i^{30}$

Step 11.3

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

$- i^{1 + 1} \cdot i^{30}$

Step 11.4

Add $1$ and $1$ .

$- i^{2} \cdot i^{30}$

Step 12

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

$- - 1 \cdot i^{30}$

Step 13

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{30}$

Step 14

Multiply $i^{30}$ by $1$ .

$i^{30}$

Step 15

Rewrite $i^{30}$ as ${(i^{4})}^{7} i^{2}$ .

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Step 15.1

Factor out $i^{28}$ .

$i^{28} i^{2}$

Step 15.2

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

${(i^{4})}^{7} i^{2}$

Step 16

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

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Step 16.1

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

${({(i^{2})}^{2})}^{7} i^{2}$

Step 16.2

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

${({(- 1)}^{2})}^{7} i^{2}$

Step 16.3

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

$1^{7} i^{2}$

Step 17

One to any power is one.

$1 i^{2}$

Step 18

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

$i^{2}$

Step 19

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

$- 1$