Simplify i^11i^13i^7*i^9

$i^{11} \cdot i^{13} \cdot i^{7} \cdot i^{9}$

Rewrite $i^{11}$ as ${(i^{4})}^{2} (i^{2} \cdot i)$ .

Factor out $i^{8}$ .

$i^{8} i^{3} \cdot i^{13} \cdot i^{7} \cdot i^{9}$

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

${(i^{4})}^{2} i^{3} \cdot i^{13} \cdot i^{7} \cdot i^{9}$

Factor out $i^{2}$ .

${(i^{4})}^{2} (i^{2} \cdot i) \cdot i^{13} \cdot i^{7} \cdot i^{9}$

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

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

${({(i^{2})}^{2})}^{2} (i^{2} \cdot i) \cdot i^{13} \cdot i^{7} \cdot i^{9}$

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

${({(- 1)}^{2})}^{2} (i^{2} \cdot i) \cdot i^{13} \cdot i^{7} \cdot i^{9}$

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

$1^{2} (i^{2} \cdot i) \cdot i^{13} \cdot i^{7} \cdot i^{9}$

One to any power is one.

$1 (i^{2} \cdot i) \cdot i^{13} \cdot i^{7} \cdot i^{9}$

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

$i^{2} \cdot i \cdot i^{13} \cdot i^{7} \cdot i^{9}$

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

$- 1 \cdot i \cdot i^{13} \cdot i^{7} \cdot i^{9}$

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

$- i \cdot i^{13} \cdot i^{7} \cdot i^{9}$

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

Factor out $i^{12}$ .

$- i \cdot (i^{12} i) \cdot i^{7} \cdot i^{9}$

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

$- i \cdot ({(i^{4})}^{3} i) \cdot i^{7} \cdot i^{9}$

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

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

$- i \cdot ({({(i^{2})}^{2})}^{3} i) \cdot i^{7} \cdot i^{9}$

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

$- i \cdot ({({(- 1)}^{2})}^{3} i) \cdot i^{7} \cdot i^{9}$

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

$- i \cdot (1^{3} i) \cdot i^{7} \cdot i^{9}$

One to any power is one.

$- i \cdot (1 i) \cdot i^{7} \cdot i^{9}$

Multiply $i$ by $1$ .

$- i \cdot i \cdot i^{7} \cdot i^{9}$

Multiply $- i i$ .

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

$- (i^{1} i) \cdot i^{7} \cdot i^{9}$

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

$- (i^{1} i^{1}) \cdot i^{7} \cdot i^{9}$

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

$- i^{1 + 1} \cdot i^{7} \cdot i^{9}$

Add $1$ and $1$ .

$- i^{2} \cdot i^{7} \cdot i^{9}$

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

$- - 1 \cdot i^{7} \cdot i^{9}$

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{7} \cdot i^{9}$

Multiply $i^{7}$ by $1$ .

$i^{7} \cdot i^{9}$

Rewrite $i^{7}$ as $i^{4} (i^{2} \cdot i)$ .

Factor out $i^{4}$ .

$i^{4} i^{3} \cdot i^{9}$

Factor out $i^{2}$ .

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

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

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

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

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

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

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

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

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

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

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

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

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

$- i \cdot i^{9}$

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

Factor out $i^{8}$ .

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

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

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

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

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

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

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

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

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

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

One to any power is one.

$- i \cdot (1 i)$

Multiply $i$ by $1$ .

$- i \cdot i$

Multiply $- i i$ .

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

$- (i^{1} i)$

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

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

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

$- i^{1 + 1}$

Add $1$ and $1$ .

$- i^{2}$

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

$- - 1$

Multiply $- 1$ by $- 1$ .

$1$

Simplify i^11*i^13*i^7*i^9

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Simplify i^11i^13i^7*i^9