Solved Examples of the Quotient of Powers Property (Grade 8)

📚 Quick Study Guide

• ➗ The Quotient of Powers Property states that when dividing powers with the same base, you subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.
• 🔢 This property only applies when the bases are the same. For example, $\frac{2^5}{2^2}$ can be simplified, but $\frac{2^5}{3^2}$ cannot directly use this property.
• 💡 Remember that $a^0 = 1$ (any non-zero number raised to the power of 0 is 1). This can often appear when applying the quotient rule!
• ✍️ Be careful with negative exponents! If $m - n$ is negative, you may need to rewrite the expression using positive exponents: $a^{-n} = \frac{1}{a^n}$.

Practice Quiz

1. What is the simplified form of $\frac{5^7}{5^3}$?
   1. $5^4$
   2. $5^{10}$
   3. $5^{21}$
   4. $5^{\frac{7}{3}}$
2. Simplify the expression $\frac{x^{12}}{x^4}$.
   1. $x^3$
   2. $x^8$
   3. $x^{16}$
   4. $x^{48}$
3. What is the result of $\frac{3^5}{3^5}$?
   1. $3$
   2. $0$
   3. $1$
   4. $3^{10}$
4. Simplify $\frac{a^9}{a^{11}}$.
   1. $a^2$
   2. $\frac{1}{a^2}$
   3. $a^{-20}$
   4. $1$
5. Evaluate $\frac{2^{10}}{2^7}$.
   1. $2^3$
   2. $2^{17}$
   3. $2^{\frac{10}{7}}$
   4. $2^{-3}$
6. Simplify $\frac{y^{15}}{y^0}$.
   1. $y^{15}$
   2. $0$
   3. $1$
   4. $y$
7. What is the simplified form of $\frac{4^6}{4^2}$?
   1. $4^3$
   2. $4^4$
   3. $4^8$
   4. $4^{12}$