Simplify i^9*1

$i^{9} \cdot 1$

Step 1

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

Factor out $i^{8}$ .

$i^{8} i \cdot 1$

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

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

Step 2

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

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

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

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

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

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

$1^{2} i \cdot 1$

Step 3

Multiply $1^{2}$ by $1$ by adding the exponents.

Move $1$ .

$1 \cdot 1^{2} i$

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

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

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

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

$1^{1 + 2} i$

Add $1$ and $2$ .

$1^{3} i$

Step 4

One to any power is one.

$1 i$

Step 5

Multiply $i$ by $1$ .

$i$