Algebra Examples

$i^{- 15}$

Step 1

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

$\frac{1}{i^{15}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $i^{15}$ as ${(i^{4})}^{3} (i^{2} \cdot i)$ .

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Step 2.1.1

Factor out $i^{12}$ .

$\frac{1}{i^{12} i^{3}}$

Step 2.1.2

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

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

Step 2.1.3

Factor out $i^{2}$ .

$\frac{1}{{(i^{4})}^{3} (i^{2} \cdot i)}$

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.3

One to any power is one.

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

Step 2.4

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

$\frac{1}{i^{2} \cdot i}$

Step 2.5

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

$\frac{1}{- 1 \cdot i}$

Step 2.6

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

$\frac{1}{- i}$

Step 3

Cancel the common factor of $1$ and $- 1$ .

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Step 3.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{- i}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{1}{i}$