Evaluate i^29i^17i^32

$i^{29} \cdot i^{17} \cdot i^{32}$

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

Factor out $i^{28}$ .

$i^{28} i \cdot i^{17} \cdot i^{32}$

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

${(i^{4})}^{7} i \cdot i^{17} \cdot i^{32}$

${(i^{4})}^{7} i \cdot i^{17} \cdot i^{32}$

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

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

${({(i^{2})}^{2})}^{7} i \cdot i^{17} \cdot i^{32}$

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

${({(- 1)}^{2})}^{7} i \cdot i^{17} \cdot i^{32}$

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

$1^{7} i \cdot i^{17} \cdot i^{32}$

$1^{7} i \cdot i^{17} \cdot i^{32}$

One to any power is one.

$1 i \cdot i^{17} \cdot i^{32}$

Multiply $i$ by $1$ .

$i \cdot i^{17} \cdot i^{32}$

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

Factor out $i^{16}$ .

$i \cdot (i^{16} i) \cdot i^{32}$

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

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

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

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

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

$i \cdot ({({(i^{2})}^{2})}^{4} i) \cdot i^{32}$

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

$i \cdot ({({(- 1)}^{2})}^{4} i) \cdot i^{32}$

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

$i \cdot (1^{4} i) \cdot i^{32}$

$i \cdot (1^{4} i) \cdot i^{32}$

One to any power is one.

$i \cdot (1 i) \cdot i^{32}$

Multiply $i$ by $1$ .

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

Multiply $i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

$- 1 \cdot i^{32}$

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

$- 1 \cdot {(i^{4})}^{8}$

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

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

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

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

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

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

$- 1 \cdot 1^{8}$

$- 1 \cdot 1^{8}$

One to any power is one.

$- 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- 1$

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