3-4 Part 0: 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 raised to non-negative integer powers.

To multiply two monomials, multiply their coefficients and add their exponents for like bases. For example, $$(5x^3)(-3x^5) = -15x^{3+5} = -15x^8$$ .

The quotient rule states that when dividing two monomials with the same base, subtract the exponent of the denominator from the exponent of the numerator. For example, $$\frac{a^m}{a^n} = a^{m-n}$$ .

$$3xy^2$$ .

When multiplying monomials, you add the exponents of like bases. For example, $$x^a \times x^b = x^{a+b}$$ .

When dividing monomials, you subtract the exponents of like bases. For example, $$\frac{x^a}{x^b} = x^{a-b}$$ .

$$x^{4-2} = x^2$$ .

To multiply a monomial by a polynomial, distribute the monomial to each term of the polynomial. For example, $$3x(2x^2 + 4x + 5) = 6x^3 + 12x^2 + 15x$$ .

$$6x^{2+3} = 6x^5$$ .

$$-3b^{3-1} = -3b^2$$ .