Let’s solve each problem step by step using exponent rules. I’ll go one at a time and make sure the math is correct before giving the final answer.
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1. (x⁴)²
When you raise a power to another power, multiply the exponents:
x⁴ˣ² = x⁸
✔ Final:
x⁸
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2. x⁻⁸
Negative exponent means take reciprocal:
1/x⁸
✔ Final:
1/x⁸
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3. (a²)⁰
Anything (except zero) raised to the 0 power is 1:
(a²)⁰ = 1
✔ Final:
1
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4. 2a² · 3b
Multiply coefficients: 2 × 3 = 6
Variables stay as they are since no like bases to combine:
6a²b
✔ Final:
6a²b
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5. (4x²)⁻⁴
First, apply negative exponent: 1/(4x²)⁴
Now raise each part inside to 4th power:
4⁴ = 256, (x²)⁴ = x⁸ → so 1/(256x⁸)
✔ Final:
1/(256x⁸)
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6. (4a⁴)²
Square both coefficient and variable:
4² = 16, (a⁴)² = a⁸ → 16a⁸
✔ Final:
16a⁸
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7. (4ab)⁻¹
Negative exponent → reciprocal:
1/(4ab)
✔ Final:
1/(4ab)
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8. (a²b⁻¹)²
Apply exponent 2 to each part:
(a²)² = a⁴, (b⁻¹)² = b⁻² → a⁴b⁻²
Rewrite with positive exponents: a⁴/b²
✔ Final:
a⁴/b²
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9. (6ab)²
Square everything:
6² = 36, a², b² → 36a²b²
✔ Final:
36a²b²
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10. 18a³ / 4a
Simplify numbers: 18/4 = 9/2
Simplify variables: a³/a = a²
So: (9/2)a² or 9a²/2
✔ Final:
9a²/2
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11. 2a³ / a²
Subtract exponents: a³/a² = a¹ = a
So: 2a
✔ Final:
2a
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12. (3a²b⁷ / a)⁵
First simplify inside: a²/a = a → so (3ab⁷)⁵
Now raise each part to 5th power:
3⁵ = 243, a⁵, (b⁷)⁵ = b³⁵ → 243a⁵b³⁵
✔ Final:
243a⁵b³⁵
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13. a⁻¹ / a⁻⁸
When dividing powers with same base, subtract exponents:
a⁻¹⁻⁽⁻⁸⁾ = a⁻¹⁺⁸ = a⁷
✔ Final:
a⁷
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14. x⁵y⁴ / xy³
x⁵/x = x⁴, y⁴/y³ = y¹ = y → x⁴y
✔ Final:
x⁴y
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15. -(9a)⁰
Anything (except 0) to the 0 power is 1 → (9a)⁰ = 1
Then apply the negative sign: -1
✔ Final:
-1
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16. 1 / 2⁻⁶
Negative exponent in denominator → move to numerator:
2⁶ = 64
✔ Final:
64
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17. a⁸ · a⁻⁷
Add exponents when multiplying same base:
a⁸⁺⁽⁻⁷⁾ = a¹ = a
✔ Final:
a
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18. (a²b)⁴
Raise each part to 4th power:
(a²)⁴ = a⁸, b⁴ → a⁸b⁴
✔ Final:
a⁸b⁴
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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
Parent Tip: Review the logic above to help your child master the concept of exponent rules worksheet answer key.
