Algebra Examples

$i^{12} \cdot 3 i^{2} \cdot 2 i^{8}$

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

${({(- 1)}^{2})}^{3} \cdot (3 i^{2}) \cdot (2 i^{8})$

Step 2.3

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

$1^{3} \cdot (3 i^{2}) \cdot (2 i^{8})$

Step 3

One to any power is one.

$1 \cdot (3 i^{2}) \cdot (2 i^{8})$

Step 4

Multiply $3 i^{2}$ by $1$ .

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

Step 5

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

$3 \cdot - 1 \cdot (2 i^{8})$

Step 6

Multiply $3$ by $- 1$ .

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

Step 7

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

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

Step 8

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

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Step 8.1

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

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

Step 8.2

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

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

Step 8.3

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

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

Step 9

One to any power is one.

$- 3 \cdot (2 \cdot 1)$

Step 10

Multiply $- 3 (2 \cdot 1)$ .

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Step 10.1

Multiply $2$ by $1$ .

$- 3 \cdot 2$

Step 10.2

Multiply $- 3$ by $2$ .

$- 6$