Evaluate i^9i^25i^12*i^16

$i^{9} \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 1

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

Factor out $i^{8}$ .

$i^{8} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

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

${(i^{4})}^{2} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 2

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

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

${({(i^{2})}^{2})}^{2} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

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

${({(- 1)}^{2})}^{2} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

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

$1^{2} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 3

One to any power is one.

$1 i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 4

Multiply $i$ by $1$ .

$i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 5

Rewrite $i^{25}$ as ${(i^{4})}^{6} i$ .

Factor out $i^{24}$ .

$i \cdot (i^{24} i) \cdot i^{12} \cdot i^{16}$

Rewrite $i^{24}$ as ${(i^{4})}^{6}$ .

$i \cdot ({(i^{4})}^{6} i) \cdot i^{12} \cdot i^{16}$

Step 6

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

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

$i \cdot ({({(i^{2})}^{2})}^{6} i) \cdot i^{12} \cdot i^{16}$

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

$i \cdot ({({(- 1)}^{2})}^{6} i) \cdot i^{12} \cdot i^{16}$

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

$i \cdot (1^{6} i) \cdot i^{12} \cdot i^{16}$

Step 7

One to any power is one.

$i \cdot (1 i) \cdot i^{12} \cdot i^{16}$

Step 8

Multiply $i$ by $1$ .

$i \cdot i \cdot i^{12} \cdot i^{16}$

Step 9

Multiply $i i$ .

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

$i^{1} i \cdot i^{12} \cdot i^{16}$

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

$i^{1} i^{1} \cdot i^{12} \cdot i^{16}$

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

$i^{1 + 1} \cdot i^{12} \cdot i^{16}$

Add $1$ and $1$ .

$i^{2} \cdot i^{12} \cdot i^{16}$

Step 10

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

$- 1 \cdot i^{12} \cdot i^{16}$

Step 11

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

$- 1 \cdot {(i^{4})}^{3} \cdot i^{16}$

Step 12

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

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

$- 1 \cdot {({(i^{2})}^{2})}^{3} \cdot i^{16}$

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

$- 1 \cdot {({(- 1)}^{2})}^{3} \cdot i^{16}$

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

$- 1 \cdot 1^{3} \cdot i^{16}$

Step 13

One to any power is one.

$- 1 \cdot 1 \cdot i^{16}$

Step 14

Multiply $- 1$ by $1$ .

$- 1 \cdot i^{16}$

Step 15

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

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

Step 16

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

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

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

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

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

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

$- 1 \cdot 1^{4}$

Step 17

One to any power is one.

$- 1 \cdot 1$

Step 18

Multiply $- 1$ by $1$ .

$- 1$

Evaluate i^9*i^25*i^12*i^16

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Evaluate i^9i^25i^12*i^16