Evaluate i^44*i^14

$i^{44} \cdot i^{14}$

Step 1

Rewrite $i^{44}$ as ${(i^{4})}^{11}$ .

${(i^{4})}^{11} \cdot i^{14}$

Step 2

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

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

${({(i^{2})}^{2})}^{11} \cdot i^{14}$

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

${({(- 1)}^{2})}^{11} \cdot i^{14}$

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

$1^{11} \cdot i^{14}$

$1^{11} \cdot i^{14}$

Step 3

One to any power is one.

$1 \cdot i^{14}$

Step 4

Multiply $i^{14}$ by $1$ .

$i^{14}$

Step 5

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

Factor out $i^{12}$ .

$i^{12} i^{2}$

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

${(i^{4})}^{3} i^{2}$

${(i^{4})}^{3} i^{2}$

Step 6

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

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

${({(i^{2})}^{2})}^{3} i^{2}$

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

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

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

$1^{3} i^{2}$

$1^{3} i^{2}$

Step 7

One to any power is one.

$1 i^{2}$

Step 8

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

$i^{2}$

Step 9

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

$- 1$

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