Simplify i^5i^36i^29

$i^{5} \cdot i^{36} \cdot i^{29}$

Factor out $i^{4}$ .

$i^{4} i \cdot i^{36} \cdot i^{29}$

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

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

${(i^{2})}^{2} i \cdot i^{36} \cdot i^{29}$

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

${(- 1)}^{2} i \cdot i^{36} \cdot i^{29}$

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

$1 i \cdot i^{36} \cdot i^{29}$

$1 i \cdot i^{36} \cdot i^{29}$

Multiply $i$ by $1$ .

$i \cdot i^{36} \cdot i^{29}$

Rewrite $i^{36}$ as ${(i^{4})}^{9}$ .

$i \cdot {(i^{4})}^{9} \cdot i^{29}$

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

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

$i \cdot {({(i^{2})}^{2})}^{9} \cdot i^{29}$

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

$i \cdot {({(- 1)}^{2})}^{9} \cdot i^{29}$

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

$i \cdot 1^{9} \cdot i^{29}$

$i \cdot 1^{9} \cdot i^{29}$

One to any power is one.

$i \cdot 1 \cdot i^{29}$

Multiply $i$ by $1$ .

$i \cdot i^{29}$

Rewrite $i^{29}$ as ${(i^{4})}^{7} i$ .

Factor out $i^{28}$ .

$i \cdot (i^{28} i)$

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

$i \cdot ({(i^{4})}^{7} i)$

$i \cdot ({(i^{4})}^{7} i)$

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

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

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

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

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

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

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

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

One to any power is one.

$i \cdot (1 i)$

Multiply $i$ by $1$ .

$i \cdot i$

Multiply $i i$ .

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

$i^{1} i$

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

$i^{1} i^{1}$

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

$i^{1 + 1}$

Add $1$ and $1$ .

$i^{2}$

$i^{2}$

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

$- 1$

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