Simplify i^13i^23i^9

$i^{13} \cdot i^{23} \cdot i^{9}$

Rewrite $i^{13}$ as ${(i^{4})}^{3} i$ .

Factor out $i^{12}$ .

$i^{12} i \cdot i^{23} \cdot i^{9}$

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

${(i^{4})}^{3} i \cdot i^{23} \cdot i^{9}$

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

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

${({(i^{2})}^{2})}^{3} i \cdot i^{23} \cdot i^{9}$

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

${({(- 1)}^{2})}^{3} i \cdot i^{23} \cdot i^{9}$

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

$1^{3} i \cdot i^{23} \cdot i^{9}$

One to any power is one.

$1 i \cdot i^{23} \cdot i^{9}$

Multiply $i$ by $1$ .

$i \cdot i^{23} \cdot i^{9}$

Rewrite $i^{23}$ as ${(i^{4})}^{5} (i^{2} \cdot i)$ .

Factor out $i^{20}$ .

$i \cdot (i^{20} i^{3}) \cdot i^{9}$

Rewrite $i^{20}$ as ${(i^{4})}^{5}$ .

$i \cdot ({(i^{4})}^{5} i^{3}) \cdot i^{9}$

Factor out $i^{2}$ .

$i \cdot ({(i^{4})}^{5} (i^{2} \cdot i)) \cdot i^{9}$

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

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

$i \cdot ({({(i^{2})}^{2})}^{5} (i^{2} \cdot i)) \cdot i^{9}$

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

$i \cdot ({({(- 1)}^{2})}^{5} (i^{2} \cdot i)) \cdot i^{9}$

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

$i \cdot (1^{5} (i^{2} \cdot i)) \cdot i^{9}$

One to any power is one.

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

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

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

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

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

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

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

Multiply $i (- i)$ .

Raise $i$ to the power of $1$ .

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

Raise $i$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- i^{1 + 1} \cdot i^{9}$

Add $1$ and $1$ .

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

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

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

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{9}$

Multiply $i^{9}$ by $1$ .

$i^{9}$

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

Factor out $i^{8}$ .

$i^{8} i$

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

${(i^{4})}^{2} i$

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

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

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

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

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

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

$1^{2} i$

One to any power is one.

$1 i$

Multiply $i$ by $1$ .

$i$

Simplify i^13*i^23*i^9

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Simplify i^13i^23i^9