Simplify i^6i^19i^39

$i^{6} \cdot i^{19} \cdot i^{39}$

Factor out $i^{4}$ .

$i^{4} i^{2} \cdot i^{19} \cdot i^{39}$

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

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

${(i^{2})}^{2} i^{2} \cdot i^{19} \cdot i^{39}$

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

${(- 1)}^{2} i^{2} \cdot i^{19} \cdot i^{39}$

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

$1 i^{2} \cdot i^{19} \cdot i^{39}$

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

$i^{2} \cdot i^{19} \cdot i^{39}$

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

$- 1 \cdot i^{19} \cdot i^{39}$

Rewrite $i^{19}$ as ${(i^{4})}^{4} (i^{2} \cdot i)$ .

Factor out $i^{16}$ .

$- 1 \cdot (i^{16} i^{3}) \cdot i^{39}$

Rewrite $i^{16}$ as ${(i^{4})}^{4}$ .

$- 1 \cdot ({(i^{4})}^{4} i^{3}) \cdot i^{39}$

Factor out $i^{2}$ .

$- 1 \cdot ({(i^{4})}^{4} (i^{2} \cdot i)) \cdot i^{39}$

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

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

$- 1 \cdot ({({(i^{2})}^{2})}^{4} (i^{2} \cdot i)) \cdot i^{39}$

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

$- 1 \cdot ({({(- 1)}^{2})}^{4} (i^{2} \cdot i)) \cdot i^{39}$

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

$- 1 \cdot (1^{4} (i^{2} \cdot i)) \cdot i^{39}$

One to any power is one.

$- 1 \cdot (1 (i^{2} \cdot i)) \cdot i^{39}$

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

$- 1 \cdot (i^{2} \cdot i) \cdot i^{39}$

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

$- 1 \cdot (- 1 \cdot i) \cdot i^{39}$

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

$- 1 \cdot (- i) \cdot i^{39}$

Multiply $- 1$ by $- 1$ .

$1 i \cdot i^{39}$

Multiply $i$ by $1$ .

$i \cdot i^{39}$

Rewrite $i^{39}$ as ${(i^{4})}^{9} (i^{2} \cdot i)$ .

Factor out $i^{36}$ .

$i \cdot (i^{36} i^{3})$

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

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

Factor out $i^{2}$ .

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

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

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

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

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

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

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

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

One to any power is one.

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

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

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

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

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

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

$i \cdot (- i)$

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^6*i^19*i^39

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Simplify i^6i^19i^39