📚 Topic Summary
Dividing monomials involves applying the quotient rule of exponents, which states that when dividing like bases, you subtract the exponents. Remember to also divide the coefficients. For example, to divide $6x^5$ by $3x^2$, you divide the coefficients (6 ÷ 3 = 2) and subtract the exponents (5 - 2 = 3), resulting in $2x^3$.
Keep an eye on negative exponents! A negative exponent means you should take the reciprocal of the base. For example, $x^{-2} = \frac{1}{x^2}$. This is super useful for simplifying expressions with negative exponents in the quotient.
🧠 Part A: Vocabulary
Match the terms on the left with their definitions on the right:
| Term |
Definition |
| 1. Coefficient |
a. A term with variables and exponents. |
| 2. Exponent |
b. The number multiplied by the variable in an algebraic expression. |
| 3. Monomial |
c. Indicates how many times to multiply the base by itself. |
| 4. Variable |
d. A symbol (usually a letter) representing an unknown value. |
| 5. Quotient Rule |
e. $a^m / a^n = a^{m-n}$ |
✍️ Part B: Fill in the Blanks
Complete the paragraph with the correct terms:
When dividing monomials, you first divide the __________. Then, for variables with the same __________, you __________ the exponents. If you end up with a __________ exponent, remember to rewrite it using a __________. This ensures your answer is fully simplified.
🤔 Part C: Critical Thinking
Explain in your own words how to simplify the expression $\frac{12a^4b^3}{4a^2b}$ and why each step is important.