Correct. Monomials are divided by dividing the coefficients and dividing the variables. When you have the same variable, you can subtract the exponents.

$\displaystyle\frac{{{49}{{x}}^{{5}}{{y}}^{{2}}}}{{{7}{{x}}^{{2}}{{y}}^{{2}}}}=\frac{{49}}{{7}}\cdot\frac{{{{x}}^{{5}}}}{{{{x}}^{{2}}}}\cdot\frac{{{{y}}^{{2}}}}{{{{y}}^{{2}}}}={7}\cdot{{x}}^{{3}}\cdot{1}={7}{{x}}^{{3}}\usepackage{cmbright}\Huge\$

The exponent for the variable x is 3.