Evaluate i^20i^32i^19

$i^{20} \cdot i^{32} \cdot i^{19}$

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

${(i^{4})}^{5} \cdot i^{32} \cdot i^{19}$

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

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

${({(i^{2})}^{2})}^{5} \cdot i^{32} \cdot i^{19}$

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

${({(- 1)}^{2})}^{5} \cdot i^{32} \cdot i^{19}$

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

$1^{5} \cdot i^{32} \cdot i^{19}$

$1^{5} \cdot i^{32} \cdot i^{19}$

One to any power is one.

$1 \cdot i^{32} \cdot i^{19}$

Multiply $i^{32}$ by $1$ .

$i^{32} \cdot i^{19}$

Rewrite $i^{32}$ as ${(i^{4})}^{8}$ .

${(i^{4})}^{8} \cdot i^{19}$

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

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

${({(i^{2})}^{2})}^{8} \cdot i^{19}$

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

${({(- 1)}^{2})}^{8} \cdot i^{19}$

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

$1^{8} \cdot i^{19}$

$1^{8} \cdot i^{19}$

One to any power is one.

$1 \cdot i^{19}$

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 $i^{2}$ .

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

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

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 $2$ .

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

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

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 $- i$ .

$- i$

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