Test questions for the power of a power property in exponents

📚 Quick Study Guide

• 🔢 Definition: The power of a power property states that to raise a power to another power, you multiply the exponents.
• 📝 Formula: $(a^m)^n = a^{m \cdot n}$, where $a$ is the base, and $m$ and $n$ are exponents.
• 💡 Example 1: $(2^3)^2 = 2^{3 \cdot 2} = 2^6 = 64$
• 🧮 Example 2: $(x^4)^5 = x^{4 \cdot 5} = x^{20}$
• 🧪 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. $35$