Evaluate i^25*i^44

$i^{25} \cdot i^{44}$

Step 1

Rewrite $i^{25}$ as ${(i^{4})}^{6} i$ .

Factor out $i^{24}$ .

$i^{24} i \cdot i^{44}$

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

${(i^{4})}^{6} i \cdot i^{44}$

${(i^{4})}^{6} i \cdot i^{44}$

Step 2

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

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

${({(i^{2})}^{2})}^{6} i \cdot i^{44}$

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

${({(- 1)}^{2})}^{6} i \cdot i^{44}$

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

$1^{6} i \cdot i^{44}$

$1^{6} i \cdot i^{44}$

Step 3

One to any power is one.

$1 i \cdot i^{44}$

Step 4

Multiply $i$ by $1$ .

$i \cdot i^{44}$

Step 5

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

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

Step 6

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

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

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

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

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

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

$i \cdot 1^{11}$

$i \cdot 1^{11}$

Step 7

One to any power is one.

$i \cdot 1$

Step 8

Multiply $i$ by $1$ .

$i$

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