Algebra Examples

$4 i^{15} \cdot 5 i^{6}$

Step 1

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

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Step 1.1

Factor out $i^{12}$ .

$4 (i^{12} i^{3}) \cdot (5 i^{6})$

Step 1.2

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

$4 ({(i^{4})}^{3} i^{3}) \cdot (5 i^{6})$

Step 1.3

Factor out $i^{2}$ .

$4 ({(i^{4})}^{3} (i^{2} \cdot i)) \cdot (5 i^{6})$

Step 2

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

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Step 2.1

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

$4 ({({(i^{2})}^{2})}^{3} (i^{2} \cdot i)) \cdot (5 i^{6})$

Step 2.2

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

$4 ({({(- 1)}^{2})}^{3} (i^{2} \cdot i)) \cdot (5 i^{6})$

Step 2.3

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

$4 (1^{3} (i^{2} \cdot i)) \cdot (5 i^{6})$

Step 3

One to any power is one.

$4 (1 (i^{2} \cdot i)) \cdot (5 i^{6})$

Step 4

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

$4 (i^{2} \cdot i) \cdot (5 i^{6})$

Step 5

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

$4 (- 1 \cdot i) \cdot (5 i^{6})$

Step 6

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

$4 (- i) \cdot (5 i^{6})$

Step 7

Multiply $- 1$ by $4$ .

$- 4 i \cdot (5 i^{6})$

Step 8

Factor out $i^{4}$ .

$- 4 i \cdot (5 (i^{4} i^{2}))$

Step 9

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

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Step 9.1

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

$- 4 i \cdot (5 ({(i^{2})}^{2} i^{2}))$

Step 9.2

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

$- 4 i \cdot (5 ({(- 1)}^{2} i^{2}))$

Step 9.3

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

$- 4 i \cdot (5 (1 i^{2}))$

Step 10

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

$- 4 i \cdot (5 i^{2})$

Step 11

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

$- 4 i \cdot (5 \cdot - 1)$

Step 12

Multiply $5$ by $- 1$ .

$- 4 i \cdot - 5$

Step 13

Multiply $- 5$ by $- 4$ .

$20 i$