Divide monomials

Learning Objectives Define a monomial and identify its components (coefficient, variable, exponent). Recall and apply the Quotient of Powers property to simplify expressions. Apply the Zero Exponent property to simplify terms. Apply the Negative Exponent property to express answers with positive exponents. Divide the coefficients and variable parts of monomials separately. Simplify complex expressions involving the division of monomials with multiple variables. Ever wondered how scientists simplify huge calculations for things like the density of a planet? 🪐 It often starts with the simple rules you'll learn here for dividing monomials! In this tutorial, you will learn the fundamental rules for dividing monomials. Mastering this skill is crucial as it forms the buildi...

TermDefinitionExample MonomialAn algebraic expression consisting of a single term, which is a product of a number (the coefficient) and one or more variables raised to non-negative integer exponents.In `7x³y`, the entire expression is a monomial. CoefficientThe numerical factor of a monomial.In `-5a²`, the coefficient is `-5`. BaseThe number or variable that is raised to a power.In `x⁴`, the base is `x`. ExponentA number indicating how many times to multiply the base by itself.In `x⁴`, the exponent is `4`. QuotientThe result obtained by dividing one quantity by another.The quotient of `15x² ÷ 3x` is `5x`.

Quotient of Powers Property \frac{x^a}{x^b} = x^{a-b}, \text{ where } x \neq 0 When dividing two powers with the same base, you keep the base and subtract the exponent of the denominator from the exponent of the numerator. Zero Exponent Property x^0 = 1, \text{ where } x \neq 0 Any non-zero base raised to the power of zero is equal to 1. This often occurs when you divide a term by itself, like `x³/x³ = x⁰ = 1`. Negative Exponent Property x^{-n} = \frac{1}{x^n}, \text{ where } x \neq 0 A negative exponent indicates a reciprocal. To make the exponent positive, move the base from the numerator to the denominator (or vice versa) and change the exponent's sign.