You're working on a
Laws of Exponents worksheet focusing on the
Power Rule.
---
✔ Power Rule Reminder:
When you raise a power to another power, you
multiply the exponents:
>
(a^m)^n = a^(m·n)
Also, if there’s a
product inside the parentheses, like `(x^a y^b)^n`, then
each factor gets raised to the outer exponent:
>
(x^a y^b)^n = x^(a·n) · y^(b·n)
And remember:
>
Any non-zero number to the 0 power is 1: `a^0 = 1` (as long as `a ≠ 0`)
---
Now let’s solve each problem step by step.
---
## 🔹 Left Column:
1. `(x²)²`
→ Multiply exponents: 2 × 2 = 4
✔ Answer: x⁴
---
2. `(x²)³`
→ 2 × 3 = 6
✔ Answer: x⁶
---
3. `(x²)⁶`
→ 2 × 6 = 12
✔ Answer: x¹²
---
4. `(y³)²`
→ 3 × 2 = 6
✔ Answer: y⁶
---
5. `(x⁴)⁰`
→ Any non-zero base to the 0 power is 1
✔ Answer: 1
*(Note: x⁴ is not zero unless x=0, but in algebra, we assume variables are such that expressions are defined — so this is 1.)*
---
## 🔹 Right Column:
6. `(x² y²)³`
→ Apply exponent to each factor:
x^(2×3) · y^(2×3) = x⁶ y⁶
✔ Answer: x⁶ y⁶
---
7. `(x² y⁴)⁵`
→ x^(2×5) · y^(4×5) = x¹⁰ y²⁰
✔ Answer: x¹⁰ y²⁰
---
8. `(x y⁴)³`
→ x^(1×3) · y^(4×3) = x³ y¹²
✔ Answer: x³ y¹²
---
9. `(x y⁶)⁴`
→ x^(1×4) · y^(6×4) = x⁴ y²⁴
✔ Answer: x⁴ y²⁴
---
10. `(x⁰)⁵`
→ First, x⁰ = 1 (for x ≠ 0), then 1⁵ = 1
✔ Answer: 1
*(Alternatively: (x⁰)⁵ = x^(0×5) = x⁰ = 1 — same result.)*
---
##
✔ Final Answers:
Left Column:
1. x⁴
2. x⁶
3. x¹²
4. y⁶
5. 1
Right Column:
6. x⁶ y⁶
7. x¹⁰ y²⁰
8. x³ y¹²
9. x⁴ y²⁴
10. 1
---
Let me know if you’d like to see these explained with visual diagrams or practice more problems! 📚
Parent Tip: Review the logic above to help your child master the concept of exponent properties worksheet.
