Simplify i^9i^6i^8

$i^{9} \cdot i^{6} \cdot i^{8}$

Step 1

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

Factor out $i^{8}$ .

$i^{8} i \cdot i^{6} \cdot i^{8}$

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

${(i^{4})}^{2} i \cdot i^{6} \cdot i^{8}$

${(i^{4})}^{2} i \cdot i^{6} \cdot i^{8}$

Step 2

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

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

${({(i^{2})}^{2})}^{2} i \cdot i^{6} \cdot i^{8}$

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

${({(- 1)}^{2})}^{2} i \cdot i^{6} \cdot i^{8}$

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

$1^{2} i \cdot i^{6} \cdot i^{8}$

$1^{2} i \cdot i^{6} \cdot i^{8}$

Step 3

One to any power is one.

$1 i \cdot i^{6} \cdot i^{8}$

Step 4

Multiply $i$ by $1$ .

$i \cdot i^{6} \cdot i^{8}$

Step 5

Factor out $i^{4}$ .

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

Step 6

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

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

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

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

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

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

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

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

Step 7

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

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

Step 8

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

$i \cdot - 1 \cdot i^{8}$

Step 9

Move $- 1$ to the left of $i$ .

$- 1 \cdot i \cdot i^{8}$

Step 10

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

$- i \cdot i^{8}$

Step 11

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

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

Step 12

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

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

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

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

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

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

$- i \cdot 1^{2}$

$- i \cdot 1^{2}$

Step 13

One to any power is one.

$- i \cdot 1$

Step 14

Multiply $- 1$ by $1$ .

$- i$

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