Simplify i^8*1

$i^{8} \cdot 1$

Step 1

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

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

Step 2

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

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

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

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

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

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

$1^{2} \cdot 1$

Step 3

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

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

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

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

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

$1^{2 + 1}$

Add $2$ and $1$ .

$1^{3}$

Step 4

One to any power is one.

$1$