Find the Exact Value 5^3i^9

$5^{3} i^{9}$

Step 1

Raise $5$ to the power of $3$ .

$125 i^{9}$

Step 2

Rewrite $i^{9}$ as ${(i^{4})}^{2} i$ .

Factor out $i^{8}$ .

$125 (i^{8} i)$

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

$125 ({(i^{4})}^{2} i)$

$125 ({(i^{4})}^{2} i)$

Step 3

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

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

$125 ({({(i^{2})}^{2})}^{2} i)$

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

$125 ({({(- 1)}^{2})}^{2} i)$

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

$125 (1^{2} i)$

$125 (1^{2} i)$

Step 4

One to any power is one.

$125 (1 i)$

Step 5

Multiply $i$ by $1$ .

$125 i$

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