Simplify (i^3)^5

${(i^{3})}^{5}$

Step 1

Factor out $i^{2}$ .

${(i^{2} \cdot i)}^{5}$

Step 2

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

${(- 1 \cdot i)}^{5}$

Step 3

Rewrite $- 1 i$ as $- i$ .

${(- i)}^{5}$

Step 4

Apply the product rule to $- i$ .

${(- 1)}^{5} i^{5}$

Step 5

Raise $- 1$ to the power of $5$ .

$- i^{5}$

Step 6

Factor out $i^{4}$ .

$- (i^{4} i)$

Step 7

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

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

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

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

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

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

$- (1 i)$

$- (1 i)$

Step 8

Multiply $i$ by $1$ .

$- i$

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