Simplify (i^5i^2i^8)^0

${(i^{5} \cdot i^{2} \cdot i^{8})}^{0}$

Factor out $i^{4}$ .

${(i^{4} i \cdot i^{2} \cdot i^{8})}^{0}$

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

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

${({(i^{2})}^{2} i \cdot i^{2} \cdot i^{8})}^{0}$

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

${({(- 1)}^{2} i \cdot i^{2} \cdot i^{8})}^{0}$

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

${(1 i \cdot i^{2} \cdot i^{8})}^{0}$

${(1 i \cdot i^{2} \cdot i^{8})}^{0}$

Multiply $i$ by $1$ .

${(i \cdot i^{2} \cdot i^{8})}^{0}$

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

${(i \cdot - 1 \cdot i^{8})}^{0}$

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

${(- 1 \cdot i \cdot i^{8})}^{0}$

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

${(- i \cdot i^{8})}^{0}$

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

${(- i \cdot {(i^{4})}^{2})}^{0}$

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

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

${(- i \cdot {({(i^{2})}^{2})}^{2})}^{0}$

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

${(- i \cdot {({(- 1)}^{2})}^{2})}^{0}$

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

${(- i \cdot 1^{2})}^{0}$

${(- i \cdot 1^{2})}^{0}$

One to any power is one.

${(- i \cdot 1)}^{0}$

Multiply $- 1$ by $1$ .

${(- i)}^{0}$

Apply the product rule to $- i$ .

${(- 1)}^{0} i^{0}$

Anything raised to $0$ is $1$ .

$1 i^{0}$

Multiply $i^{0}$ by $1$ .

$i^{0}$

Anything raised to $0$ is $1$ .

$1$

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