Simplify i^66

$i^{66}$

Step 1

Rewrite $i^{66}$ as ${(i^{4})}^{16} i^{2}$ .

Factor out $i^{64}$ .

$i^{64} i^{2}$

Rewrite $i^{64}$ as ${(i^{4})}^{16}$ .

${(i^{4})}^{16} i^{2}$

${(i^{4})}^{16} i^{2}$

Step 2

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

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

${({(i^{2})}^{2})}^{16} i^{2}$

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

${({(- 1)}^{2})}^{16} i^{2}$

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

$1^{16} i^{2}$

$1^{16} i^{2}$

Step 3

One to any power is one.

$1 i^{2}$

Step 4

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

$i^{2}$

Step 5

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

$- 1$

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