Dividing Monomials

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables.

The quotient rule states that when dividing two powers with the same base, subtract the exponent of the denominator from the exponent of the numerator: $$a^m / a^n = a^{m-n}$$ .

$$x^{5-2} = x^3$$ .

$$y^{8-3} = y^5$$ .

When you divide a variable by itself, the result is 1, as long as the variable is not zero: $$\frac{x}{x} = 1$$ .

$$\frac{10}{5} \times x^{6-2} = 2x^4$$ .

The result is $$\frac{1}{a^{n-m}}$$ , which is a fraction with a positive exponent.

$$1$$ .

$$\frac{3}{6} \times x^{4-2} = \frac{1}{2}x^2$$ .

$$\frac{12}{4} \times a^{3-2} \times b^{2-1} = 3ab$$ .