Evaluate i^6i^38i^25

$i^{6} \cdot i^{38} \cdot i^{25}$

Step 1

Factor out $i^{4}$ .

$i^{4} i^{2} \cdot i^{38} \cdot i^{25}$

Step 2

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

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

${(i^{2})}^{2} i^{2} \cdot i^{38} \cdot i^{25}$

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

${(- 1)}^{2} i^{2} \cdot i^{38} \cdot i^{25}$

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

$1 i^{2} \cdot i^{38} \cdot i^{25}$

$1 i^{2} \cdot i^{38} \cdot i^{25}$

Step 3

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

$i^{2} \cdot i^{38} \cdot i^{25}$

Step 4

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

$- 1 \cdot i^{38} \cdot i^{25}$

Step 5

Rewrite $i^{38}$ as ${(i^{4})}^{9} i^{2}$ .

Factor out $i^{36}$ .

$- 1 \cdot (i^{36} i^{2}) \cdot i^{25}$

Rewrite $i^{36}$ as ${(i^{4})}^{9}$ .

$- 1 \cdot ({(i^{4})}^{9} i^{2}) \cdot i^{25}$

$- 1 \cdot ({(i^{4})}^{9} i^{2}) \cdot i^{25}$

Step 6

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

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

$- 1 \cdot ({({(i^{2})}^{2})}^{9} i^{2}) \cdot i^{25}$

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

$- 1 \cdot ({({(- 1)}^{2})}^{9} i^{2}) \cdot i^{25}$

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

$- 1 \cdot (1^{9} i^{2}) \cdot i^{25}$

$- 1 \cdot (1^{9} i^{2}) \cdot i^{25}$

Step 7

One to any power is one.

$- 1 \cdot (1 i^{2}) \cdot i^{25}$

Step 8

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

$- 1 \cdot i^{2} \cdot i^{25}$

Step 9

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

$- 1 \cdot - 1 \cdot i^{25}$

Step 10

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{25}$

Step 11

Multiply $i^{25}$ by $1$ .

$i^{25}$

Step 12

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

Factor out $i^{24}$ .

$i^{24} i$

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

${(i^{4})}^{6} i$

${(i^{4})}^{6} i$

Step 13

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

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

${({(i^{2})}^{2})}^{6} i$

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

${({(- 1)}^{2})}^{6} i$

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

$1^{6} i$

$1^{6} i$

Step 14

One to any power is one.

$1 i$

Step 15

Multiply $i$ by $1$ .

$i$

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