Test Your Knowledge: Quotient Rule of Exponents Questions

📚 Quick Study Guide

• ➗ The Quotient Rule: When dividing exponents with the same base, subtract the exponents.
• 📝 Formula: $\frac{a^m}{a^n} = a^{m-n}$ (where a ≠ 0).
• 🔢 Example 1: $\frac{x^5}{x^2} = x^{5-2} = x^3$
• 💡 Example 2: $\frac{4y^7}{2y^3} = 2y^{7-3} = 2y^4$
• 🚫 Important Note: The base ('a' in the formula) must be the same for the quotient rule to apply.

🧪 Practice Quiz

1. What is the simplified form of $\frac{x^{10}}{x^2}$?
   1. $x^5$
   2. $x^8$
   3. $x^{12}$
   4. $x^{20}$
2. Simplify: $\frac{y^6}{y^6}$?
   1. $y^{12}$
   2. $y$
   3. 1
   4. 0
3. What is the result of $\frac{z^9}{z^3}$?
   1. $z^3$
   2. $z^6$
   3. $z^{12}$
   4. $z^{27}$
4. Simplify: $\frac{a^{15}}{a^5}$?
   1. $a^3$
   2. $a^{10}$
   3. $a^{20}$
   4. $a^{75}$
5. What does $\frac{b^4}{b}$ equal?
   1. $b^4$
   2. 4
   3. $b^3$
   4. 1
6. Simplify the expression: $\frac{5c^8}{c^2}$?
   1. $5c^4$
   2. $5c^6$
   3. $4c^6$
   4. $5c^{10}$
7. $\frac{d^{12}}{d^4}$ is equivalent to which of the following?
   1. $d^3$
   2. $d^8$
   3. $d^{16}$
   4. $d^{48}$