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Integer Exponent Properties Guide

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Integer Exponent Properties Guide worksheet preview

Integer Exponent Properties Guide

Mathematical exponents illustration

📚 Part 1: Key Properties Review

Remember these important exponent properties:

Product Rule: a^m × a^n = a^(m+n)

Quotient Rule: a^m ÷ a^n = a^(m-n)

Power Rule: (a^m)^n = a^(m×n)

Zero Exponent: a^0 = 1 (when a ≠ 0)

Negative Exponent: a^(-n) = 1/a^n

1. Which property would you use to simplify 3^4 × 3^2?

Product Rule

Quotient Rule

Power Rule

Zero Exponent Rule

2. What does 5^(-3) equal?

-15

1/5^3

-5^3

5^3

3. Simplify: 2^6 ÷ 2^4

2^2

2^10

2^24

1

✏️ Part 2: Practice Problems

Simplify each expression. Write your final answer in exponential form with positive exponents.

4. 4^3 × 4^5 = __________
5. (6^2)^4 = __________
6. 7^8 ÷ 7^3 = __________
7. 9^(-2) = __________
8. 3^0 × 3^7 = __________

🎯 Part 3: Challenge Problems

9. Simplify: (2^3)^2 × 2^(-4)

Show your work step by step:

Final answer: __________

10. Explain why 8^0 = 1 in your own words:
11. Marcus says that 5^(-3) = -5^3. Is he correct? Explain your reasoning:

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