Precalculus Examples

$i^{4} + i^{- 12}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

${(i^{2})}^{2} + i^{- 12}$

Step 1.1.2

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

${(- 1)}^{2} + i^{- 12}$

Step 1.1.3

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

$1 + i^{- 12}$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$1 + \frac{1}{i^{12}}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

$1 + \frac{1}{{(i^{4})}^{3}}$

Step 1.3.2

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

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Step 1.3.2.1

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

$1 + \frac{1}{{({(i^{2})}^{2})}^{3}}$

Step 1.3.2.2

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

$1 + \frac{1}{{({(- 1)}^{2})}^{3}}$

Step 1.3.2.3

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

$1 + \frac{1}{1^{3}}$

Step 1.3.3

One to any power is one.

$1 + \frac{1}{1}$

Step 1.4

Divide $1$ by $1$ .

$1 + 1$

Step 2

Add $1$ and $1$ .

$2$