Simplify (x^(7/2))/(x^3)

$\frac{x^{\frac{7}{2}}}{x^{3}}$

Move $x^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{7}{2}} x^{- 3}$

Multiply $x^{\frac{7}{2}}$ by $x^{- 3}$ by adding the exponents.

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

$x^{\frac{7}{2} - 3}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{7}{2} - 3 \cdot \frac{2}{2}}$

Combine $- 3$ and $\frac{2}{2}$ .

$x^{\frac{7}{2} + \frac{- 3 \cdot 2}{2}}$

Combine the numerators over the common denominator.

$x^{\frac{7 - 3 \cdot 2}{2}}$

Simplify the numerator.

Multiply $- 3$ by $2$ .

$x^{\frac{7 - 6}{2}}$

Subtract $6$ from $7$ .

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