Algebra Examples

${(- 4 i)}^{11}$

Step 1

Apply the product rule to $- 4 i$ .

${(- 4)}^{11} i^{11}$

Step 2

Raise $- 4$ to the power of $11$ .

$- 4194304 i^{11}$

Step 3

Rewrite $i^{11}$ as ${(i^{4})}^{2} (i^{2} \cdot i)$ .

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Step 3.1

Factor out $i^{8}$ .

$- 4194304 (i^{8} i^{3})$

Step 3.2

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

$- 4194304 ({(i^{4})}^{2} i^{3})$

Step 3.3

Factor out $i^{2}$ .

$- 4194304 ({(i^{4})}^{2} (i^{2} \cdot i))$

Step 4

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

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Step 4.1

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

$- 4194304 ({({(i^{2})}^{2})}^{2} (i^{2} \cdot i))$

Step 4.2

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

$- 4194304 ({({(- 1)}^{2})}^{2} (i^{2} \cdot i))$

Step 4.3

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

$- 4194304 (1^{2} (i^{2} \cdot i))$

Step 5

One to any power is one.

$- 4194304 (1 (i^{2} \cdot i))$

Step 6

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

$- 4194304 (i^{2} \cdot i)$

Step 7

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

$- 4194304 (- 1 \cdot i)$

Step 8

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

$- 4194304 (- i)$

Step 9

Multiply $- 1$ by $- 4194304$ .

$4194304 i$