ryan_diaz
ryan_diaz 2d ago • 10 views

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

Hey everyone! 👋 Let's conquer the Quotient of Powers Property together. It's all about simplifying exponents when you're dividing! ➗ Check out the guide and quiz below to become a pro! 😄
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📚 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. $4^{12}$
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