📚 Topic Summary
Dividing monomials involves applying the rules of exponents. Specifically, when dividing monomials with the same base, you subtract the exponents. Remember, a monomial is a single term expression consisting of numbers, variables, and non-negative integer exponents. When dividing, simplify coefficients separately and apply the exponent rule to each variable.
🧠 Part A: Vocabulary
Match the term with its definition:
- Term: Coefficient
- Term: Exponent
- Term: Monomial
- Term: Variable
- Term: Base
- Definition: A symbol representing a quantity that can change or vary.
- Definition: A number or expression that is multiplied by itself.
- Definition: A number multiplied by a variable in an algebraic term.
- Definition: An expression with only one term.
- Definition: A quantity representing the power to which a given number or expression is to be raised.
✏️ Part B: Fill in the Blanks
When dividing monomials with the same ________, you ________ the exponents. For example, to simplify $\frac{x^5}{x^2}$, you would subtract 2 from 5, resulting in $x^{_____}$. Remember to also ________ any numerical coefficients separately.
🤔 Part C: Critical Thinking
Explain in your own words how the quotient rule for exponents works and provide an example demonstrating its application. Be sure to discuss why the bases must be the same for the rule to apply.