Properties of Exponents: True or False | Worksheet - Free Printable

1. 3³ · 3⁴ = 3⁷ → True (3³ · 3⁴ = 3^(3+4) = 3⁷)
2. (8³)⁴ = 8⁷ → False ( (8³)⁴ = 8^(3×4) = 8¹² )
3. 4² · 4³ = 4⁵ → True (4² · 4³ = 4^(2+3) = 4⁵)
4. 9⁵/3 = 9⁴ → False (9⁵/3 = 9⁵ / 3¹ = 9⁵ / 3, not 9⁴)
5. 5⁶ · 5⁵ = 5¹¹ → True (5⁶ · 5⁵ = 5^(6+5) = 5¹¹)
6. 1 = 2⁰ → True (Any non-zero number to the power of 0 is 1)
7. (2³)² = 2⁶ → True ((2³)² = 2^(3×2) = 2⁶)
8. 6⁻¹ = 1/6 → True (a⁻ⁿ = 1/aⁿ)
9. 9⁴ · 9³ = 9⁷ → True (9⁴ · 9³ = 9^(4+3) = 9⁷)
10. 6⁰/6 = 6¹ → False (6⁰/6 = 1/6, not 6)
11. (7³)⁴ = 7¹² → True ((7³)⁴ = 7^(3×4) = 7¹²)
12. 1/2³ · 2⁴ = 2¹ → True (1/2³ · 2⁴ = 2⁻³ · 2⁴ = 2^(⁻³⁺⁴) = 2¹)
13. (4²)³ = 4⁶ → True ((4²)³ = 4^(2×3) = 4⁶)
14. 12⁴/12² = 12² → True (12⁴/12² = 12^(4-2) = 12²)
15. 4⁰ · 4⁻⁵ = 4⁻⁵ → True (4⁰ · 4⁻⁵ = 1 · 4⁻⁵ = 4⁻⁵)

Challenge:
False equations to correct:
4. 9⁵/3 = 9⁴ → 9⁵/9 = 9⁴ → 9⁵/9¹ = 9⁴ → 9⁴ = 9⁴ (Correct)
10. 6⁰/6 = 6¹ → 6⁰/6 = 1/6 → 1/6 = 6¹ → 1/6 = 6 → Change to 6⁰/6 = 6⁻¹
14. 12⁴/12² = 12² → 12⁴/12² = 12² → 12² = 12² (Correct)
15. 4⁰ · 4⁻⁵ = 4⁻⁵ → 4⁰ · 4⁻⁵ = 4⁻⁵ → 1 · 4⁻⁵ = 4⁻⁵ → 4⁻⁵ = 4⁻⁵ (Correct)

The only false equation that needs correction is:
4. 9⁵/3 = 9⁴ → Change 3 to 9: 9⁵/9 = 9⁴
10. 6⁰/6 = 6¹ → Change 6¹ to 6⁻¹: 6⁰/6 = 6⁻¹