Online quiz: Evaluate expressions with integer exponents (Grade 8 test)

📚 Quick Study Guide

• 🔢 An exponent indicates how many times a base number is multiplied by itself.
• ➕ For any non-zero number $a$ and integers $m$ and $n$: $a^m \cdot a^n = a^{m+n}$ (Product of Powers).
• ➗ For any non-zero number $a$ and integers $m$ and $n$: $\frac{a^m}{a^n} = a^{m-n}$ (Quotient of Powers).
• 💡 For any non-zero number $a$ and integer $n$: $(a^m)^n = a^{m \cdot n}$ (Power of a Power).
• 📌 For any non-zero number $a$: $a^0 = 1$ (Zero Exponent).
• ➖ For any non-zero number $a$ and integer $n$: $a^{-n} = \frac{1}{a^n}$ (Negative Exponent).

✍️ Practice Quiz

1. What is the value of $2^{-3}$?
   1. $\frac{1}{8}$
   2. $-8$
   3. $8$
   4. $\frac{1}{6}$
2. Simplify: $x^5 \cdot x^{-2}$
   1. $x^3$
   2. $x^{-10}$
   3. $x^{-7}$
   4. $x^7$
3. What is the value of $(3^2)^0$?
   1. $1$
   2. $0$
   3. $9$
   4. $6$
4. Simplify: $\frac{y^7}{y^3}$
   1. $y^4$
   2. $y^{10}$
   3. $y^{-4}$
   4. $y^{21}$
5. What is the value of $(-5)^2$?
   1. $25$
   2. $-25$
   3. $10$
   4. $-10$
6. Simplify: $(2a^3)^2$
   1. $4a^6$
   2. $2a^6$
   3. $4a^5$
   4. $2a^5$
7. What is the value of $4^{-1} + 2^{-2}$?
   1. $\frac{1}{2}$
   2. $\frac{1}{16}$
   3. $\frac{2}{3}$
   4. $\frac{1}{3}$