Evaluate i^6*i^6

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

Step 1

Factor out $i^{4}$ .

$i^{4} i^{2} \cdot i^{6}$

Step 2

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

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

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

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

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

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

$1 i^{2} \cdot i^{6}$

$1 i^{2} \cdot i^{6}$

Step 3

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

$i^{2} \cdot i^{6}$

Step 4

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

$- 1 \cdot i^{6}$

Step 5

Factor out $i^{4}$ .

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

Step 6

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

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

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

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

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

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

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

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

Step 7

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

$- 1 \cdot i^{2}$

Step 8

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

$- 1 \cdot - 1$

Step 9

Multiply $- 1$ by $- 1$ .

$1$

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