nelson.jennifer89
nelson.jennifer89 1d ago โ€ข 0 views

Test questions for the power of a power property in exponents

Hey there! ๐Ÿ‘‹ Get ready to boost your exponent skills with this quick guide and quiz on the power of a power property! Let's make math fun! ๐Ÿค“
๐Ÿงฎ Mathematics

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veronica_andrews Dec 30, 2025

๐Ÿ“š Quick Study Guide

  • ๐Ÿ”ข Definition: The power of a power property states that to raise a power to another power, you multiply the exponents.
  • ๐Ÿ“ Formula: $(a^m)^n = a^{m \cdot n}$, where $a$ is the base, and $m$ and $n$ are exponents.
  • ๐Ÿ’ก Example 1: $(2^3)^2 = 2^{3 \cdot 2} = 2^6 = 64$
  • ๐Ÿงฎ Example 2: $(x^4)^5 = x^{4 \cdot 5} = x^{20}$
  • ๐Ÿงช Important Note: This property only applies when you are raising a power to another power.

Practice Quiz

  1. What is the simplified form of $(3^2)^3$?
    1. $3^5$
    2. $3^6$
    3. $9^6$
    4. $3^8$
  2. Simplify $(x^5)^4$.
    1. $x^9$
    2. $x^{20}$
    3. $x^{-1}$
    4. $4x^5$
  3. What is the value of $(2^4)^2$?
    1. $2^6$
    2. $2^8$
    3. $4^8$
    4. $2^{16}$
  4. Simplify $(a^{-2})^3$.
    1. $a^{-5}$
    2. $a^{-6}$
    3. $a^1$
    4. $a^{-8}$
  5. What is the simplified form of $((5^2)^0)^7$?
    1. $5^{14}$
    2. $5^9$
    3. $1$
    4. $5^0$
  6. Simplify $(b^3)^{-2}$.
    1. $b^1$
    2. $b^{-6}$
    3. $b^5$
    4. $b^{-1}$
  7. What is the value of $(7^1)^2 \cdot (7^0)^5$?
    1. $49$
    2. $14$
    3. $7$
    4. $35$
Click to see Answers
  1. B
  2. B
  3. B
  4. B
  5. C
  6. B
  7. A

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