Simplify i^20i^25i^23*i^18

$i^{20} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

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

${(i^{4})}^{5} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

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

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

${({(i^{2})}^{2})}^{5} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

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

${({(- 1)}^{2})}^{5} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

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

$1^{5} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

One to any power is one.

$1 \cdot i^{25} \cdot i^{23} \cdot i^{18}$

Multiply $i^{25}$ by $1$ .

$i^{25} \cdot i^{23} \cdot i^{18}$

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

Factor out $i^{24}$ .

$i^{24} i \cdot i^{23} \cdot i^{18}$

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

${(i^{4})}^{6} i \cdot i^{23} \cdot i^{18}$

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

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

${({(i^{2})}^{2})}^{6} i \cdot i^{23} \cdot i^{18}$

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

${({(- 1)}^{2})}^{6} i \cdot i^{23} \cdot i^{18}$

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

$1^{6} i \cdot i^{23} \cdot i^{18}$

One to any power is one.

$1 i \cdot i^{23} \cdot i^{18}$

Multiply $i$ by $1$ .

$i \cdot i^{23} \cdot i^{18}$

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

Factor out $i^{20}$ .

$i \cdot (i^{20} i^{3}) \cdot i^{18}$

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

$i \cdot ({(i^{4})}^{5} i^{3}) \cdot i^{18}$

Factor out $i^{2}$ .

$i \cdot ({(i^{4})}^{5} (i^{2} \cdot i)) \cdot i^{18}$

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

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

$i \cdot ({({(i^{2})}^{2})}^{5} (i^{2} \cdot i)) \cdot i^{18}$

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

$i \cdot ({({(- 1)}^{2})}^{5} (i^{2} \cdot i)) \cdot i^{18}$

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

$i \cdot (1^{5} (i^{2} \cdot i)) \cdot i^{18}$

One to any power is one.

$i \cdot (1 (i^{2} \cdot i)) \cdot i^{18}$

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

$i \cdot (i^{2} \cdot i) \cdot i^{18}$

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

$i \cdot (- 1 \cdot i) \cdot i^{18}$

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

$i \cdot (- i) \cdot i^{18}$

Multiply $i (- i)$ .

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

$- (i^{1} i) \cdot i^{18}$

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

$- (i^{1} i^{1}) \cdot i^{18}$

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

$- i^{1 + 1} \cdot i^{18}$

Add $1$ and $1$ .

$- i^{2} \cdot i^{18}$

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

$- - 1 \cdot i^{18}$

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{18}$

Multiply $i^{18}$ by $1$ .

$i^{18}$

Rewrite $i^{18}$ as ${(i^{4})}^{4} i^{2}$ .

Factor out $i^{16}$ .

$i^{16} i^{2}$

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

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

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

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

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

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

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

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

$1^{4} i^{2}$

One to any power is one.

$1 i^{2}$

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

$i^{2}$

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

$- 1$

Simplify i^20*i^25*i^23*i^18

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Simplify i^20i^25i^23*i^18