Quizizz worksheet on properties of exponents featuring 15 multiple-choice questions for simplifying algebraic expressions with exponents.

Let’s solve each of the first 5 problems step by step using properties of exponents.

---

Problem 1: Simplify

Expression: \( 5x^9 \cdot -6x^2 \)

✔ Step 1: Multiply the coefficients (numbers):
\( 5 \cdot (-6) = -30 \)

✔ Step 2: Multiply the variables with exponents — when multiplying like bases, add the exponents:
\( x^9 \cdot x^2 = x^{9+2} = x^{11} \)

✔ Final Answer: \( -30x^{11} \)

✔️ Correct Choice: C

---

Problem 2: Simplify

Expression: \( (5x^{11})^2 \)

✔ Use the power of a product rule: \( (ab)^n = a^n b^n \)
So, \( (5x^{11})^2 = 5^2 \cdot (x^{11})^2 \)

✔ Calculate each part:
- \( 5^2 = 25 \)
- \( (x^{11})^2 = x^{11 \cdot 2} = x^{22} \) (power of a power: multiply exponents)

✔ Final Answer: \( 25x^{22} \)

✔️ Correct Choice: C

---

Problem 3: Simplify

Expression: \( (x^8)(x^{-5}) \)

✔ When multiplying like bases, add the exponents:
\( x^8 \cdot x^{-5} = x^{8 + (-5)} = x^{3} \)

✔ Final Answer: \( x^3 \)

✔️ Correct Choice: D

---

Problem 4: Simplify

Expression: \( (k^2)^5 \)

✔ Use the power of a power rule: \( (a^m)^n = a^{m \cdot n} \)
So, \( (k^2)^5 = k^{2 \cdot 5} = k^{10} \)

✔ Final Answer: \( k^{10} \)

✔️ Correct Choice: D

---

✔ Final Answers:

1. C – \( -30x^{11} \)
2. C – \( 25x^{22} \)
3. D – \( x^3 \)
4. D – \( k^{10} \)

Let me know if you’d like help with questions 5–15 too!