Algebra Examples

$i^{- 13}$

Step 1

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

$\frac{1}{i^{13}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $i^{13}$ as ${(i^{4})}^{3} i$ .

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Step 2.1.1

Factor out $i^{12}$ .

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

Step 2.1.2

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.3

One to any power is one.

$\frac{1}{1 i}$

Step 2.4

Multiply $i$ by $1$ .

$\frac{1}{i}$