Simplify (x^(1/2))/(x^(3/2))

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

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

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

Simplify the denominator.

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

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

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $3$ .

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

Divide $2$ by $2$ .

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

Simplify $x^{1}$ .

$\frac{1}{x}$