Simplify i^8*i^60

$i^{8} \cdot i^{60}$

Step 1

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

${(i^{4})}^{2} \cdot i^{60}$

Step 2

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

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

${({(i^{2})}^{2})}^{2} \cdot i^{60}$

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

${({(- 1)}^{2})}^{2} \cdot i^{60}$

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

$1^{2} \cdot i^{60}$

$1^{2} \cdot i^{60}$

Step 3

One to any power is one.

$1 \cdot i^{60}$

Step 4

Multiply $i^{60}$ by $1$ .

$i^{60}$

Step 5

Rewrite $i^{60}$ as ${(i^{4})}^{15}$ .

${(i^{4})}^{15}$

Step 6

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

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

${({(i^{2})}^{2})}^{15}$

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

${({(- 1)}^{2})}^{15}$

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

$1^{15}$

$1^{15}$

Step 7

One to any power is one.

$1$

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