Simplify i^14i^8i^24*i^12

$i^{14} \cdot i^{8} \cdot i^{24} \cdot i^{12}$

Step 1

Rewrite $i^{14}$ as ${(i^{4})}^{3} i^{2}$ .

Factor out $i^{12}$ .

$i^{12} i^{2} \cdot i^{8} \cdot i^{24} \cdot i^{12}$

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

${(i^{4})}^{3} i^{2} \cdot i^{8} \cdot i^{24} \cdot i^{12}$

Step 2

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

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

${({(i^{2})}^{2})}^{3} i^{2} \cdot i^{8} \cdot i^{24} \cdot i^{12}$

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

${({(- 1)}^{2})}^{3} i^{2} \cdot i^{8} \cdot i^{24} \cdot i^{12}$

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

$1^{3} i^{2} \cdot i^{8} \cdot i^{24} \cdot i^{12}$

Step 3

One to any power is one.

$1 i^{2} \cdot i^{8} \cdot i^{24} \cdot i^{12}$

Step 4

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

$i^{2} \cdot i^{8} \cdot i^{24} \cdot i^{12}$

Step 5

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

$- 1 \cdot i^{8} \cdot i^{24} \cdot i^{12}$

Step 6

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

$- 1 \cdot {(i^{4})}^{2} \cdot i^{24} \cdot i^{12}$

Step 7

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

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

$- 1 \cdot {({(i^{2})}^{2})}^{2} \cdot i^{24} \cdot i^{12}$

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

$- 1 \cdot {({(- 1)}^{2})}^{2} \cdot i^{24} \cdot i^{12}$

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

$- 1 \cdot 1^{2} \cdot i^{24} \cdot i^{12}$

Step 8

One to any power is one.

$- 1 \cdot 1 \cdot i^{24} \cdot i^{12}$

Step 9

Multiply $- 1$ by $1$ .

$- 1 \cdot i^{24} \cdot i^{12}$

Step 10

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

$- 1 \cdot {(i^{4})}^{6} \cdot i^{12}$

Step 11

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

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

$- 1 \cdot {({(i^{2})}^{2})}^{6} \cdot i^{12}$

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

$- 1 \cdot {({(- 1)}^{2})}^{6} \cdot i^{12}$

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

$- 1 \cdot 1^{6} \cdot i^{12}$

Step 12

One to any power is one.

$- 1 \cdot 1 \cdot i^{12}$

Step 13

Multiply $- 1$ by $1$ .

$- 1 \cdot i^{12}$

Step 14

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

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

Step 15

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

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

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

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

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

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

$- 1 \cdot 1^{3}$

Step 16

One to any power is one.

$- 1 \cdot 1$

Step 17

Multiply $- 1$ by $1$ .

$- 1$

Simplify i^14*i^8*i^24*i^12

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Simplify i^14i^8i^24*i^12