Evaluate i^9i^9i^21*i^28

$i^{9} \cdot i^{9} \cdot i^{21} \cdot i^{28}$

Rewrite $i^{9}$ as ${(i^{4})}^{2} i$ .

Factor out $i^{8}$ .

$i^{8} i \cdot i^{9} \cdot i^{21} \cdot i^{28}$

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

${(i^{4})}^{2} i \cdot i^{9} \cdot i^{21} \cdot i^{28}$

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

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

${({(i^{2})}^{2})}^{2} i \cdot i^{9} \cdot i^{21} \cdot i^{28}$

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

${({(- 1)}^{2})}^{2} i \cdot i^{9} \cdot i^{21} \cdot i^{28}$

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

$1^{2} i \cdot i^{9} \cdot i^{21} \cdot i^{28}$

One to any power is one.

$1 i \cdot i^{9} \cdot i^{21} \cdot i^{28}$

Multiply $i$ by $1$ .

$i \cdot i^{9} \cdot i^{21} \cdot i^{28}$

Rewrite $i^{9}$ as ${(i^{4})}^{2} i$ .

Factor out $i^{8}$ .

$i \cdot (i^{8} i) \cdot i^{21} \cdot i^{28}$

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

$i \cdot ({(i^{4})}^{2} i) \cdot i^{21} \cdot i^{28}$

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

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

$i \cdot ({({(i^{2})}^{2})}^{2} i) \cdot i^{21} \cdot i^{28}$

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

$i \cdot ({({(- 1)}^{2})}^{2} i) \cdot i^{21} \cdot i^{28}$

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

$i \cdot (1^{2} i) \cdot i^{21} \cdot i^{28}$

One to any power is one.

$i \cdot (1 i) \cdot i^{21} \cdot i^{28}$

Multiply $i$ by $1$ .

$i \cdot i \cdot i^{21} \cdot i^{28}$

Multiply $i i$ .

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

$i^{1} i \cdot i^{21} \cdot i^{28}$

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

$i^{1} i^{1} \cdot i^{21} \cdot i^{28}$

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

$i^{1 + 1} \cdot i^{21} \cdot i^{28}$

Add $1$ and $1$ .

$i^{2} \cdot i^{21} \cdot i^{28}$

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

$- 1 \cdot i^{21} \cdot i^{28}$

Rewrite $i^{21}$ as ${(i^{4})}^{5} i$ .

Factor out $i^{20}$ .

$- 1 \cdot (i^{20} i) \cdot i^{28}$

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

$- 1 \cdot ({(i^{4})}^{5} i) \cdot i^{28}$

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

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

$- 1 \cdot ({({(i^{2})}^{2})}^{5} i) \cdot i^{28}$

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

$- 1 \cdot ({({(- 1)}^{2})}^{5} i) \cdot i^{28}$

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

$- 1 \cdot (1^{5} i) \cdot i^{28}$

One to any power is one.

$- 1 \cdot (1 i) \cdot i^{28}$

Multiply $i$ by $1$ .

$- 1 \cdot i \cdot i^{28}$

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

$- i \cdot i^{28}$

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

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

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

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

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

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

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

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

$- i \cdot 1^{7}$

One to any power is one.

$- i \cdot 1$

Multiply $- 1$ by $1$ .

$- i$

Evaluate i^9*i^9*i^21*i^28

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Evaluate i^9i^9i^21*i^28