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

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

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

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

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

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

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

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $- 1$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $3$ .

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