Algebra Examples

$\frac{x^{\frac{1}{2}}}{x^{\frac{3}{2}}}$

Step 1

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

$\frac{1}{x^{\frac{3}{2}} x^{- \frac{1}{2}}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $x^{\frac{3}{2}}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

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Step 2.1.1

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

$\frac{1}{x^{\frac{3}{2} - \frac{1}{2}}}$

Step 2.1.2

Combine the numerators over the common denominator.

$\frac{1}{x^{\frac{3 - 1}{2}}}$

Step 2.1.3

Subtract $1$ from $3$ .

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

Step 2.1.4

Divide $2$ by $2$ .

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

Step 2.2

Simplify $x^{1}$ .

$\frac{1}{x}$