Simplify i^38*i^9

$i^{38} \cdot i^{9}$

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

Factor out $i^{36}$ .

$i^{36} i^{2} \cdot i^{9}$

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

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

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

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

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

${({(i^{2})}^{2})}^{9} i^{2} \cdot i^{9}$

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

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

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

$1^{9} i^{2} \cdot i^{9}$

$1^{9} i^{2} \cdot i^{9}$

One to any power is one.

$1 i^{2} \cdot i^{9}$

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

$i^{2} \cdot i^{9}$

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

$- 1 \cdot i^{9}$

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

Factor out $i^{8}$ .

$- 1 \cdot (i^{8} i)$

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

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

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

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

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

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

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

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

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

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

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

One to any power is one.

$- 1 \cdot (1 i)$

Multiply $i$ by $1$ .

$- 1 \cdot i$

Rewrite $- 1 i$ as $- i$ .

$- i$

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