Let’s solve each problem one by one. Remember: we want only
positive exponents in our final answers.
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1. (x²)⁰
Any number or variable raised to the power of 0 is 1.
→ Answer:
1
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2. (4x²)⁻⁴
Negative exponent means flip the base and make exponent positive.
= 1 / (4x²)⁴
Now apply exponent to both 4 and x²:
= 1 / (4⁴ · x⁸) = 1 / (256x⁸)
→ Answer:
1/(256x⁸)
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3. (8r⁰)⁴
First, r⁰ = 1 → so inside becomes 8·1 = 8
Then 8⁴ = 4096
→ Answer:
4096
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4. 3p² · 4p
Multiply coefficients: 3·4 = 12
Add exponents for p: p² · p¹ = p³
→ Answer:
12p³
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5. 2p³q⁻³ · 2p⁻¹q³
Multiply coefficients: 2·2 = 4
For p: p³ · p⁻¹ = p^(3-1) = p²
For q: q⁻³ · q³ = q^(-3+3) = q⁰ = 1
So we have 4p² · 1 = 4p²
→ Answer:
4p²
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6. (a²b⁻¹)²
Apply exponent to each part:
(a²)² = a⁴
(b⁻¹)² = b⁻² → move to denominator to make positive: 1/b²
So: a⁴ / b²
→ Answer:
a⁴/b²
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7. x⁻¹ / (4x⁻¹)
Both numerator and denominator have x⁻¹ → they cancel out!
Left with: 1/4
→ Answer:
1/4
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8. (2[⁴m⁻³])⁻¹
Wait — this looks like it might be a typo? Probably meant: (2⁴ m⁻³)⁻¹
Assuming that:
First, 2⁴ = 16 → so inside is 16m⁻³
Now raise to -1: 1 / (16m⁻³) = m³ / 16
→ Answer:
m³/16
*(If it was meant to be something else, please clarify — but based on standard notation, this makes sense.)*
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9. (2fg⁴)⁴(fg)⁶
Break it down:
(2fg⁴)⁴ = 2⁴ · f⁴ · g¹⁶ = 16f⁴g¹⁶
(fg)⁶ = f⁶g⁶
Now multiply together:
16f⁴g¹⁶ · f⁶g⁶ = 16 · f^(4+6) · g^(16+6) = 16f¹⁰g²²
→ Answer:
16f¹⁰g²²
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10. (2x⁴y⁻⁴) / (8x⁷y³)
Simplify coefficients: 2/8 = 1/4
x terms: x⁴ / x⁷ = x^(4-7) = x⁻³ → move to denominator: 1/x³
y terms: y⁻⁴ / y³ = y^(-4-3) = y⁻⁷ → move to denominator: 1/y⁷
So overall: 1 / (4x³y⁷)
→ Answer:
1/(4x³y⁷)
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11. -(9y)⁰
Anything to the 0 power is 1 → so (9y)⁰ = 1
Then negative sign: -1
→ Answer:
-1
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12. 1 / p⁻⁸
Negative exponent in denominator → flip to numerator: p⁸
→ Answer:
p⁸
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13. (y²)⁰
Again, anything to the 0 power is 1.
→ Answer:
1
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14. 4x³ · xy²
Coefficients: 4 (no other coefficient)
x terms: x³ · x = x⁴
y terms: y²
→ Answer:
4x⁴y²
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15. (2x²)⁻⁴
Flip because of negative exponent: 1 / (2x²)⁴
= 1 / (2⁴ · x⁸) = 1 / (16x⁸)
→ Answer:
1/(16x⁸)
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16. (4x⁴y⁻²)⁻¹
Flip entire expression: 1 / (4x⁴y⁻²)
Now handle y⁻² in denominator → moves to numerator as y²
So: y² / (4x⁴)
→ Answer:
y²/(4x⁴)
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17. (4p)⁻²
Flip: 1 / (4p)² = 1 / (16p²)
→ Answer:
1/(16p²)
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18. (2y² · 4x)⁻¹
First simplify inside: 2·4 = 8 → so (8xy²)⁻¹
Flip: 1 / (8xy²)
→ Answer:
1/(8xy²)
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Final Answer:
1. 1
2. 1/(256x⁸)
3. 4096
4. 12p³
5. 4p²
6. a⁴/b²
7. 1/4
8. m³/16
9. 16f¹⁰g²²
10. 1/(4x³y⁷)
11. -1
12. p⁸
13. 1
14. 4x⁴y²
15. 1/(16x⁸)
16. y²/(4x⁴)
17. 1/(16p²)
18. 1/(8xy²)
Parent Tip: Review the logic above to help your child master the concept of simplifying negative exponents worksheet.
