Precalculus Examples

$\frac{x^{\frac{1}{2}}}{x^{9}}$

Step 1

Move $x^{\frac{1}{2}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{1}{x^{9} x^{- \frac{1}{2}}}$

Step 2

Multiply $x^{9}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{x^{9 - \frac{1}{2}}}$

Step 2.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{x^{9 \cdot \frac{2}{2} - \frac{1}{2}}}$

Step 2.3

Combine $9$ and $\frac{2}{2}$ .

$\frac{1}{x^{\frac{9 \cdot 2}{2} - \frac{1}{2}}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{1}{x^{\frac{9 \cdot 2 - 1}{2}}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $9$ by $2$ .

$\frac{1}{x^{\frac{18 - 1}{2}}}$

Step 2.5.2

Subtract $1$ from $18$ .

$\frac{1}{x^{\frac{17}{2}}}$