Multiply and divide monomials

Learning Objectives Define a monomial and identify its components (coefficient, variable, exponent). Apply the Product of Powers rule to multiply monomials with single or multiple variables. Apply the Quotient of Powers rule to divide monomials. Simplify expressions involving coefficients, including integers and fractions. Apply the Power of a Power and Power of a Product rules to simplify monomials raised to an exponent. Simplify complex expressions that combine multiplication, division, and powers of monomials. Ever wondered how to calculate the area of a rectangle with sides `4x²` and `3x⁵`? Let's find out how simple it can be! 📐 This tutorial will teach you the fundamental rules for multiplying and dividing monomials. Mastering this skill is essential for working...

TermDefinitionExample MonomialA single term that is a number, a variable, or the product of a number and one or more variables with non-negative integer exponents.`7x²y` is a monomial. `7x + y` is not, as it has two terms. CoefficientThe numerical factor of a monomial.In the monomial `-5a³b`, the coefficient is `-5`. BaseThe variable or number being raised to a power.In the monomial `x⁷`, the base is `x`. ExponentA number indicating how many times the base is multiplied by itself.In the monomial `y⁴`, the exponent is `4`. Degree of a MonomialThe sum of the exponents of all the variables in the monomial.The degree of `3a²b⁵c` is `2 + 5 + 1 = 8`.

Product of Powers Rule a^m * a^n = a^(m+n) When multiplying two monomials with the same base, keep the base and ADD the exponents. Quotient of Powers Rule a^m / a^n = a^(m-n) (where a ≠ 0) When dividing two monomials with the same base, keep the base and SUBTRACT the exponents (numerator exponent minus denominator exponent). Power of a Power Rule (a^m)^n = a^(m*n) When raising a power to another power, keep the base and MULTIPLY the exponents. Power of a Product Rule (ab)^n = a^n * b^n To find the power of a product, apply the exponent to each factor inside the parentheses.