Simplify i^54

$i^{54}$

Step 1

Rewrite $i^{54}$ as ${(i^{4})}^{13} i^{2}$ .

Factor out $i^{52}$ .

$i^{52} i^{2}$

Rewrite $i^{52}$ as ${(i^{4})}^{13}$ .

${(i^{4})}^{13} i^{2}$

${(i^{4})}^{13} i^{2}$

Step 2

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

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

${({(i^{2})}^{2})}^{13} i^{2}$

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

${({(- 1)}^{2})}^{13} i^{2}$

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

$1^{13} i^{2}$

$1^{13} i^{2}$

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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