Simplify i^7i^28i^25*i^19

$i^{7} \cdot i^{28} \cdot i^{25} \cdot i^{19}$

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

Factor out $i^{4}$ .

$i^{4} i^{3} \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Factor out $i^{2}$ .

$i^{4} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25} \cdot i^{19}$

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

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

${(i^{2})}^{2} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25} \cdot i^{19}$

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

${(- 1)}^{2} (i^{2} \cdot i) \cdot i^{28} \cdot i^{25} \cdot i^{19}$

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

$1 (i^{2} \cdot i) \cdot i^{28} \cdot i^{25} \cdot i^{19}$

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

$i^{2} \cdot i \cdot i^{28} \cdot i^{25} \cdot i^{19}$

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

$- 1 \cdot i \cdot i^{28} \cdot i^{25} \cdot i^{19}$

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

$- i \cdot i^{28} \cdot i^{25} \cdot i^{19}$

Rewrite $i^{28}$ as ${(i^{4})}^{7}$ .

$- i \cdot {(i^{4})}^{7} \cdot i^{25} \cdot i^{19}$

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

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

$- i \cdot {({(i^{2})}^{2})}^{7} \cdot i^{25} \cdot i^{19}$

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

$- i \cdot {({(- 1)}^{2})}^{7} \cdot i^{25} \cdot i^{19}$

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

$- i \cdot 1^{7} \cdot i^{25} \cdot i^{19}$

One to any power is one.

$- i \cdot 1 \cdot i^{25} \cdot i^{19}$

Multiply $- 1$ by $1$ .

$- i \cdot i^{25} \cdot i^{19}$

Rewrite $i^{25}$ as ${(i^{4})}^{6} i$ .

Factor out $i^{24}$ .

$- i \cdot (i^{24} i) \cdot i^{19}$

Rewrite $i^{24}$ as ${(i^{4})}^{6}$ .

$- i \cdot ({(i^{4})}^{6} i) \cdot i^{19}$

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

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

$- i \cdot ({({(i^{2})}^{2})}^{6} i) \cdot i^{19}$

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

$- i \cdot ({({(- 1)}^{2})}^{6} i) \cdot i^{19}$

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

$- i \cdot (1^{6} i) \cdot i^{19}$

One to any power is one.

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

Multiply $i$ by $1$ .

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

Multiply $- i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{19}$

Multiply $i^{19}$ by $1$ .

$i^{19}$

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

Factor out $i^{16}$ .

$i^{16} i^{3}$

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

${(i^{4})}^{4} i^{3}$

Factor out $i^{2}$ .

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

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

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

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

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

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

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

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

One to any power is one.

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

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

$i^{2} \cdot i$

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

$- 1 \cdot i$

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

$- i$

Simplify i^7*i^28*i^25*i^19

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Simplify i^7i^28i^25*i^19