Evaluate i^26*i^54

$i^{26} \cdot i^{54}$

Step 1

Rewrite $i^{26}$ as ${(i^{4})}^{6} i^{2}$ .

Factor out $i^{24}$ .

$i^{24} i^{2} \cdot i^{54}$

Rewrite $i^{24}$ as ${(i^{4})}^{6}$ .

${(i^{4})}^{6} i^{2} \cdot i^{54}$

${(i^{4})}^{6} i^{2} \cdot i^{54}$

Step 2

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

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

${({(i^{2})}^{2})}^{6} i^{2} \cdot i^{54}$

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

${({(- 1)}^{2})}^{6} i^{2} \cdot i^{54}$

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

$1^{6} i^{2} \cdot i^{54}$

$1^{6} i^{2} \cdot i^{54}$

Step 3

One to any power is one.

$1 i^{2} \cdot i^{54}$

Step 4

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

$i^{2} \cdot i^{54}$

Step 5

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

$- 1 \cdot i^{54}$

Step 6

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

Factor out $i^{52}$ .

$- 1 \cdot (i^{52} i^{2})$

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

$- 1 \cdot ({(i^{4})}^{13} i^{2})$

$- 1 \cdot ({(i^{4})}^{13} i^{2})$

Step 7

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

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

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

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

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

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

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

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

Step 8

One to any power is one.

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

Step 9

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

$- 1 \cdot i^{2}$

Step 10

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

$- 1 \cdot - 1$

Step 11

Multiply $- 1$ by $- 1$ .

$1$

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