Simplify i^38*i^15

$i^{38} \cdot i^{15}$

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

Factor out $i^{36}$ .

$i^{36} i^{2} \cdot i^{15}$

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

${(i^{4})}^{9} i^{2} \cdot i^{15}$

${(i^{4})}^{9} i^{2} \cdot i^{15}$

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

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

${({(i^{2})}^{2})}^{9} i^{2} \cdot i^{15}$

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

${({(- 1)}^{2})}^{9} i^{2} \cdot i^{15}$

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

$1^{9} i^{2} \cdot i^{15}$

$1^{9} i^{2} \cdot i^{15}$

One to any power is one.

$1 i^{2} \cdot i^{15}$

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

$i^{2} \cdot i^{15}$

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

$- 1 \cdot i^{15}$

Rewrite $i^{15}$ as ${(i^{4})}^{3} (i^{2} \cdot i)$ .

Factor out $i^{12}$ .

$- 1 \cdot (i^{12} i^{3})$

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

$- 1 \cdot ({(i^{4})}^{3} i^{3})$

Factor out $i^{2}$ .

$- 1 \cdot ({(i^{4})}^{3} (i^{2} \cdot i))$

$- 1 \cdot ({(i^{4})}^{3} (i^{2} \cdot i))$

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

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

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

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

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

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

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

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

One to any power is one.

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

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

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

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

$- 1 \cdot (- 1 \cdot i)$

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

$- 1 \cdot (- i)$

Multiply $- 1$ by $- 1$ .

$1 i$

Multiply $i$ by $1$ .

$i$

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