Simplify i^34*i^14

$i^{34} \cdot i^{14}$

Rewrite $i^{34}$ as ${(i^{4})}^{8} i^{2}$ .

Factor out $i^{32}$ .

$i^{32} i^{2} \cdot i^{14}$

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

${(i^{4})}^{8} i^{2} \cdot i^{14}$

${(i^{4})}^{8} i^{2} \cdot i^{14}$

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

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

${({(i^{2})}^{2})}^{8} i^{2} \cdot i^{14}$

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

${({(- 1)}^{2})}^{8} i^{2} \cdot i^{14}$

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

$1^{8} i^{2} \cdot i^{14}$

$1^{8} i^{2} \cdot i^{14}$

One to any power is one.

$1 i^{2} \cdot i^{14}$

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

$i^{2} \cdot i^{14}$

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

$- 1 \cdot i^{14}$

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

Factor out $i^{12}$ .

$- 1 \cdot (i^{12} i^{2})$

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

$- 1 \cdot ({(i^{4})}^{3} i^{2})$

$- 1 \cdot ({(i^{4})}^{3} i^{2})$

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

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

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

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

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

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

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

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

One to any power is one.

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

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

$- 1 \cdot i^{2}$

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

$- 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

$1$

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