To solve these problems, we use the
Product Rule of Exponents. This rule states that when you multiply two expressions with the same base, you add their exponents.
The formula is:
a^m × a^n = a^(m+n)
Let’s go through each problem one by one:
---
1. 3² × 3⁶
Same base (3), so add exponents: 2 + 6 = 8
→ 3⁸
2. 4² × 4⁹
Same base (4), add exponents: 2 + 9 = 11
→ 4¹¹
3. 8² × 8⁰
Remember: any number to the power of 0 is 1. So 8⁰ = 1.
But we can still apply the rule: 2 + 0 = 2
→ 8²
4. 7³ × 7¹¹
Add exponents: 3 + 11 = 14
→ 7¹⁴
5. 6⁵ × 6
Note: 6 is the same as 6¹. So add exponents: 5 + 1 = 6
→ 6⁶
6. 2 × 2³ × 2⁶
First, write 2 as 2¹. Now all have base 2. Add exponents: 1 + 3 + 6 = 10
→ 2¹⁰
---
Now the right column:
7. x⁹ × x⁴
Same base (x), add exponents: 9 + 4 = 13
→ x¹³
8. y² × y⁷
Add exponents: 2 + 7 = 9
→ y⁹
9. b × b⁵
b is b¹, so 1 + 5 = 6
→ b⁶
10. x³ × x⁴
Add exponents: 3 + 4 = 7
→ x⁷
11. w⁴ × w
w is w¹, so 4 + 1 = 5
→ w⁵
12. x² × y³ × x⁴
Group same bases: x² × x⁴ = x⁶, and y³ stays alone.
So: x⁶ × y³ → x⁶y³
---
All calculations checked. Ready for final answer.
Final Answer:
3⁸, 4¹¹, 8², 7¹⁴, 6⁶, 2¹⁰, x¹³, y⁹, b⁶, x⁷, w⁵, x⁶y³
Parent Tip: Review the logic above to help your child master the concept of laws of exponent worksheet.
