Simplify i^25i^14i^7*i^17

$i^{25} \cdot i^{14} \cdot i^{7} \cdot i^{17}$

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

Factor out $i^{24}$ .

$i^{24} i \cdot i^{14} \cdot i^{7} \cdot i^{17}$

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

${(i^{4})}^{6} i \cdot i^{14} \cdot i^{7} \cdot i^{17}$

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

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

${({(i^{2})}^{2})}^{6} i \cdot i^{14} \cdot i^{7} \cdot i^{17}$

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

${({(- 1)}^{2})}^{6} i \cdot i^{14} \cdot i^{7} \cdot i^{17}$

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

$1^{6} i \cdot i^{14} \cdot i^{7} \cdot i^{17}$

One to any power is one.

$1 i \cdot i^{14} \cdot i^{7} \cdot i^{17}$

Multiply $i$ by $1$ .

$i \cdot i^{14} \cdot i^{7} \cdot i^{17}$

Rewrite $i^{14}$ as ${(i^{4})}^{3} i^{2}$ .

Factor out $i^{12}$ .

$i \cdot (i^{12} i^{2}) \cdot i^{7} \cdot i^{17}$

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

$i \cdot ({(i^{4})}^{3} i^{2}) \cdot i^{7} \cdot i^{17}$

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

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

$i \cdot ({({(i^{2})}^{2})}^{3} i^{2}) \cdot i^{7} \cdot i^{17}$

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

$i \cdot ({({(- 1)}^{2})}^{3} i^{2}) \cdot i^{7} \cdot i^{17}$

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

$i \cdot (1^{3} i^{2}) \cdot i^{7} \cdot i^{17}$

One to any power is one.

$i \cdot (1 i^{2}) \cdot i^{7} \cdot i^{17}$

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

$i \cdot i^{2} \cdot i^{7} \cdot i^{17}$

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

$i \cdot - 1 \cdot i^{7} \cdot i^{17}$

Move $- 1$ to the left of $i$ .

$- 1 \cdot i \cdot i^{7} \cdot i^{17}$

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

$- i \cdot i^{7} \cdot i^{17}$

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

Factor out $i^{4}$ .

$- i \cdot (i^{4} i^{3}) \cdot i^{17}$

Factor out $i^{2}$ .

$- i \cdot (i^{4} (i^{2} \cdot i)) \cdot i^{17}$

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

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

$- i \cdot ({(i^{2})}^{2} (i^{2} \cdot i)) \cdot i^{17}$

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

$- i \cdot ({(- 1)}^{2} (i^{2} \cdot i)) \cdot i^{17}$

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

$- i \cdot (1 (i^{2} \cdot i)) \cdot i^{17}$

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

$- i \cdot (i^{2} \cdot i) \cdot i^{17}$

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

$- i \cdot (- 1 \cdot i) \cdot i^{17}$

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

$- i \cdot (- i) \cdot i^{17}$

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

$1 i i \cdot i^{17}$

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

$1 (i^{1} i) \cdot i^{17}$

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

$1 (i^{1} i^{1}) \cdot i^{17}$

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

$1 i^{1 + 1} \cdot i^{17}$

Add $1$ and $1$ .

$1 i^{2} \cdot i^{17}$

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

$i^{2} \cdot i^{17}$

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

$- 1 \cdot i^{17}$

Rewrite $i^{17}$ as ${(i^{4})}^{4} i$ .

Factor out $i^{16}$ .

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

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

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

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

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

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

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

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

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

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

One to any power is one.

$- 1 \cdot (1 i)$

Multiply $i$ by $1$ .

$- 1 \cdot i$

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

$- i$

Simplify i^25*i^14*i^7*i^17

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Simplify i^25i^14i^7*i^17