Here is the solution to the worksheet on
Negative Exponents, with explanations for each problem.
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🔢 Key Rules to Remember:
1.
Negative Exponent Rule:
For any nonzero number `a` and integer `n`:
>
a⁻ⁿ = 1 / aⁿ
2.
Zero Exponent Rule:
For any nonzero number `a`:
>
a⁰ = 1
3.
Positive Exponent Rule:
Just multiply the base by itself the number of times indicated by the exponent.
4.
Even Power of Negative Number:
>
(-a)² = a² (positive result)
5.
Odd Power of Negative Number:
>
(-a)³ = -a³ (negative result)
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##
✔ Solutions with Explanations:
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Left Column:
1.
9⁻²
= 1 / 9² = 1 / 81
➤ *Negative exponent → reciprocal of positive power.*
2.
7²
= 7 × 7 = 49
➤ *Simple squaring.*
3.
7⁻³
= 1 / 7³ = 1 / 343
➤ *Negative exponent → reciprocal of cube.*
4.
10⁰
= 1
➤ *Any nonzero number to the power 0 is 1.*
5.
(-6)²
= (-6) × (-6) = 36
➤ *Even power → positive result.*
6.
5⁻¹
= 1 / 5¹ = 1/5
➤ *Negative exponent → reciprocal.*
7.
7⁻¹
= 1 / 7
➤ *Same as above.*
8.
(-4)⁰
= 1
➤ *Nonzero base to power 0 = 1.*
9.
8²
= 8 × 8 = 64
➤ *Squaring.*
10.
9⁻¹
= 1 / 9
➤ *Reciprocal.*
---
Right Column:
1.
(-6)⁰
= 1
➤ *Any nonzero number (including negative) to the 0 power is 1.*
2.
(-5)⁰
= 1
➤ *Same rule.*
3.
(-9)²
= (-9) × (-9) = 81
➤ *Even power → positive.*
4.
(-5)⁻³
= 1 / (-5)³ = 1 / (-125) =
-1/125
➤ *Negative exponent → reciprocal; odd power keeps negative sign.*
5.
(-8)²
= (-8) × (-8) = 64
➤ *Even power → positive.*
6.
(-5)⁻³ *(Repeated — same as #4)*
=
-1/125
7.
(-10)⁻¹
= 1 / (-10) =
-1/10
➤ *Negative exponent → reciprocal; negative base stays negative.*
8.
5²
= 5 × 5 = 25
➤ *Squaring.*
9.
(-7)⁻¹
= 1 / (-7) =
-1/7
➤ *Reciprocal of negative number is negative.*
10.
5² *(Repeated — same as #8)*
= 25
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## 📝 Final Answer Sheet:
| Problem | Answer |
|---------------|----------------|
| 9⁻² | 1/81 |
| 7² | 49 |
| 7⁻³ | 1/343 |
| 10⁰ | 1 |
| (-6)² | 36 |
| 5⁻¹ | 1/5 |
| 7⁻¹ | 1/7 |
| (-4)⁰ | 1 |
| 8² | 64 |
| 9⁻¹ | 1/9 |
| (-6)⁰ | 1 |
| (-5)⁰ | 1 |
| (-9)² | 81 |
| (-5)⁻³ | -1/125 |
| (-8)² | 64 |
| (-5)⁻³ | -1/125 |
| (-10)⁻¹ | -1/10 |
| 5² | 25 |
| (-7)⁻¹ | -1/7 |
| 5² | 25 |
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✔ All problems solved using exponent rules. Pay close attention to signs when dealing with negative bases and odd/even exponents!
Let me know if you’d like a printable version or step-by-step work shown!
Parent Tip: Review the logic above to help your child master the concept of exponents worksheet.
