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Negative ExponentsFREEWorksheet Generator(Grades 7-9)
Negative Exponents worksheets with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems for Grades 7–9.
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Set A • 10 Qs
PanMaths.comNegative Exponents Worksheet Generator with Answers (Reciprocal Rule) • Set A (Medium)
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 10
1.10⁻3
= ______Workspace:
2.3⁻1
= ______Workspace:
3.8⁻3
= ______Workspace:
4.6⁻1
= ______Workspace:
5.10⁻2
= ______Workspace:
6.3⁻1
= ______Workspace:
7.6⁻3
= ______Workspace:
8.4⁻1
= ______Workspace:
9.5⁻3
= ______Workspace:
10.7⁻1
= ______Workspace:
PanMaths.comAnswer Key & Worked Solutions • Set A (Medium)
Answer Key
Total Problems: 10
1.10⁻3
= 1/10001. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 10⁻3 = 1 / (10³)
3. Evaluate Denominator: 10^3 = 1000
4. Final Result: 1/1000 ✅
2.3⁻1
= 1/31. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 3⁻1 = 1 / (3^1)
3. Evaluate Denominator: 3^1 = 3
4. Final Result: 1/3 ✅
3.8⁻3
= 1/5121. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 8⁻3 = 1 / (8³)
3. Evaluate Denominator: 8^3 = 512
4. Final Result: 1/512 ✅
4.6⁻1
= 1/61. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 6⁻1 = 1 / (6^1)
3. Evaluate Denominator: 6^1 = 6
4. Final Result: 1/6 ✅
5.10⁻2
= 1/1001. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 10⁻2 = 1 / (10²)
3. Evaluate Denominator: 10^2 = 100
4. Final Result: 1/100 ✅
6.3⁻1
= 1/31. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 3⁻1 = 1 / (3^1)
3. Evaluate Denominator: 3^1 = 3
4. Final Result: 1/3 ✅
7.6⁻3
= 1/2161. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 6⁻3 = 1 / (6³)
3. Evaluate Denominator: 6^3 = 216
4. Final Result: 1/216 ✅
8.4⁻1
= 1/41. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 4⁻1 = 1 / (4^1)
3. Evaluate Denominator: 4^1 = 4
4. Final Result: 1/4 ✅
9.5⁻3
= 1/1251. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 5⁻3 = 1 / (5³)
3. Evaluate Denominator: 5^3 = 125
4. Final Result: 1/125 ✅
10.7⁻1
= 1/71. Negative Exponent Reciprocal Law: b⁻ⁿ = 1 / bⁿ
2. Apply Rule: 7⁻1 = 1 / (7^1)
3. Evaluate Denominator: 7^1 = 7
4. Final Result: 1/7 ✅
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Build Custom Test ➔The Mathematical Proof: Why Negative Exponents Mean Reciprocal
Consider the descending sequence of powers for base 2:
- 2³ = 8
- Divide by 2 ➔ 2² = 4
- Divide by 2 ➔ 2¹ = 2
- Divide by 2 ➔ 2⁰ = 1
- Divide by 2 ➔ 2⁻¹ = 1/2
- Divide by 2 ➔ 2⁻² = 1/4 = 1 / 2²
- Divide by 2 ➔ 2⁻³ = 1/8 = 1 / 2³
Each time the exponent decreases by 1, the value is divided by the base. Continuing past zero naturally creates reciprocals with positive powers in the denominator.
The Top 3 Negative Exponent Misconceptions
- Misconception 1: 3⁻² = -9.
Correction: The exponent indicates the operation (reciprocal repeated division), not a negative value. 3⁻² = 1 / 3² = 1/9. - Misconception 2: Multiplying base by exponent (e.g. 4⁻² = -8).
Correction: Exponents mean repeated multiplication/division, never simple multiplication. 4⁻² = 1 / 16. - Misconception 3: Base with negative sign vs negative exponent: (-2)³ vs 2⁻³.
Correction: (-2)³ = (-2) × (-2) × (-2) = -8 (negative result). But 2⁻³ = 1 / 2³ = 1/8 (positive fractional result).
Anti-Cheat Classroom Versions & Step-by-Step Answer Keys
To support high-integrity classroom evaluations and homeschool quizzes, PanMaths allows instant generation of Set A and Set B shuffled sets. Each page is formatted in crisp high-contrast black & white for photocopiers. The included answer key displays each step: identifying the base and negative exponent, applying the reciprocal fraction conversion, and expanding the positive power into the final simplified fraction.