Let’s work through each problem one by one using the
Power Rule for exponents.
The Power Rule says:
> When you raise a power to another power, multiply the exponents.
> Example: (x^a)^b = x^(a×b)
Also remember:
- Any nonzero number raised to the 0 power is 1.
- If there are multiple variables inside parentheses, apply the outer exponent to each variable separately.
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Left Column:
1. (x²)² → Multiply exponents: 2 × 2 = 4 →
x⁴
2. (x²)³ → 2 × 3 = 6 →
x⁶
3. (x²)⁶ → 2 × 6 = 12 →
x¹²
4. (y³)² → 3 × 2 = 6 →
y⁶
5. (x⁴)⁰ → Anything (except 0) to the 0 power is 1 →
1
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Right Column:
6. (x²y²)³ → Apply exponent 3 to both x² and y²:
x^(2×3) = x⁶, y^(2×3) = y⁶ →
x⁶y⁶
7. (x²y⁴)⁵ → x^(2×5)=x¹⁰, y^(4×5)=y²⁰ →
x¹⁰y²⁰
8. (xy⁴)³ → x^(1×3)=x³, y^(4×3)=y¹² →
x³y¹²
9. (xy⁶)⁴ → x^(1×4)=x⁴, y^(6×4)=y²⁴ →
x⁴y²⁴
10. (x⁰)⁵ → First, x⁰ = 1, then 1⁵ = 1 →
1
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All answers verified.
Final Answer:
x⁴, x⁶, x¹², y⁶, 1, x⁶y⁶, x¹⁰y²⁰, x³y¹², x⁴y²⁴, 1
Parent Tip: Review the logic above to help your child master the concept of exponent rules worksheet pdf.
