Basic Math Examples

${(- i^{2015})}^{2016}$

Step 1

Rewrite $i^{2015}$ as ${(i^{4})}^{503} (i^{2} \cdot i)$ .

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Step 1.1

Factor out $i^{2012}$ .

${(- (i^{2012} i^{3}))}^{2016}$

Step 1.2

Rewrite $i^{2012}$ as ${(i^{4})}^{503}$ .

${(- ({(i^{4})}^{503} i^{3}))}^{2016}$

Step 1.3

Factor out $i^{2}$ .

${(- ({(i^{4})}^{503} (i^{2} \cdot i)))}^{2016}$

Step 2

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

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Step 2.1

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

${(- ({({(i^{2})}^{2})}^{503} (i^{2} \cdot i)))}^{2016}$

Step 2.2

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

${(- ({({(- 1)}^{2})}^{503} (i^{2} \cdot i)))}^{2016}$

Step 2.3

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

${(- (1^{503} (i^{2} \cdot i)))}^{2016}$

Step 3

One to any power is one.

${(- (1 (i^{2} \cdot i)))}^{2016}$

Step 4

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

${(- (i^{2} \cdot i))}^{2016}$

Step 5

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

${(- (- 1 \cdot i))}^{2016}$

Step 6

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

${(- - i)}^{2016}$

Step 7

Multiply $- 1$ by $- 1$ .

${(1 i)}^{2016}$

Step 8

Multiply $i$ by $1$ .

$i^{2016}$

Step 9

Rewrite $i^{2016}$ as ${(i^{4})}^{504}$ .

${(i^{4})}^{504}$

Step 10

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

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Step 10.1

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

${({(i^{2})}^{2})}^{504}$

Step 10.2

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

${({(- 1)}^{2})}^{504}$

Step 10.3

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

$1^{504}$

Step 11

One to any power is one.

$1$