With Coefficients

When a quotient has coefficients, you divide the coefficients and subtract the exponents. In $\frac{12x^{5}}{4x^{2}}$, divide the numbers first: $\frac{12}{4} = 3$. Then apply the quotient rule to the powers: $\frac{x^{5}}{x^{2}} = x^{3}$. Put the two parts together to get $3x^{3}$.

This works the same way as multiplying terms. When you multiply, the coefficients multiply and the exponents add. When you divide, the coefficients divide and the exponents subtract. The coefficient is an ordinary factor, and the exponent is a count of factors, so the two never mix.

If the coefficients do not divide evenly, write their quotient as a fraction. For nonzero $x$, $\frac{7x^{5}}{2x^{2}} = \frac{7}{2}x^{3}$. The powers still follow the quotient rule.