Exponents Worksheets with Answer Key - Free Printable

Let’s go through each problem one by one, simplifying using exponent rules. We’ll keep it simple and clear.

---

1. (x⁴)²
When you raise a power to another power, multiply the exponents:
x⁴ˣ² = x⁸ → x⁸

2. x⁻⁸
Negative exponent means “put in denominator”:
→ 1/x⁸

3. (a²)⁰
Anything to the zero power is 1:
→ 1

4. 2a² · 3b
Multiply coefficients: 2×3 = 6
Variables stay as they are since bases differ:
→ 6a²b

5. (4x²)⁻⁴
Apply exponent to both 4 and x²:
4⁻⁴ × x⁻⁸ → 1/(4⁴x⁸) = 1/(256x⁸)
→ 1/(256x⁸)

6. (4a⁴)²
Square both 4 and a⁴:
4² = 16, (a⁴)² = a⁸ → 16a⁸

7. (4ab)⁻¹
Negative exponent → flip the whole thing:
→ 1/(4ab)

8. (a²b⁻¹)²
Apply exponent 2 to both:
(a²)² = a⁴, (b⁻¹)² = b⁻² → a⁴b⁻²
Write without negative exponent: → a⁴/b²

9. (6ab)²
Square each part: 6²=36, a², b² → 36a²b²

10. 18a³ / 4a
Simplify numbers: 18/4 = 9/2
Subtract exponents for ‘a’: a³⁻¹ = a² → (9a²)/2

11. 2a³ / a²
Subtract exponents: a³⁻² = a¹ → 2a

12. (3a²b⁷ / a)⁵
First simplify inside: a²/a = a¹ → (3ab⁷)⁵
Now apply exponent 5: 3⁵=243, a⁵, (b⁷)⁵=b³⁵ → 243a⁵b³⁵

13. a⁻¹ / a⁻⁸
Divide powers with same base → subtract exponents:
a⁻¹ ⁻ ⁽⁻⁸⁾ = a⁷ → a⁷

14. x⁵y⁴ / xy³
x⁵/x = x⁴, y⁴/y³ = y¹ → x⁴y

15. -(9a)⁰
Anything to zero power is 1, then apply the negative sign:
→ -1

16. 1 / 2⁻⁶
Negative exponent in denominator → move to numerator:
2⁶ = 64 → 64

17. a⁸ · a⁻⁷
Add exponents: a⁸⁺⁽⁻⁷⁾ = a¹ → a

18. (a²b)⁴
Apply exponent 4 to both: (a²)⁴ = a⁸, b⁴ → a⁸b⁴

---

Final Answer:
1. x⁸
2. 1/x⁸
3. 1
4. 6a²b
5. 1/(256x⁸)
6. 16a⁸
7. 1/(4ab)
8. a⁴/b²
9. 36a²b²
10. (9a²)/2
11. 2a
12. 243a⁵b³⁵
13. a⁷
14. x⁴y
15. -1
16. 64
17. a
18. a⁸b⁴