Absolutely! Let’s solve this worksheet step by step using the
Product Rule for Exponents.
---
✔ Product Rule for Exponents:
> When multiplying two powers with the
same base, you
add the exponents:
>
>
aᵐ × aⁿ = aᵐ⁺ⁿ
This rule applies
only when the bases are identical.
---
We’ll go row by row and solve each problem.
---
## 🔹 Row 1:
1.
12¹⁴ × 12² = 12¹⁴⁺² = 12¹⁶
2.
8⁵ × 8³ = 8⁵⁺³ = 8⁸
3.
13³ × 13³ = 13³⁺³ = 13⁶
---
## 🔹 Row 2:
4.
5⁸ × 5¹ = 5⁸⁺¹ = 5⁹
5.
3⁸ × 3³ = 3⁸⁺³ = 3¹¹
6.
8¹⁵ × 8³ = 8¹⁵⁺³ = 8¹⁸
---
## 🔹 Row 3:
7.
6³ × 6² = 6³⁺² = 6⁵
8.
2⁷ × 2² = 2⁷⁺² = 2⁹
9.
16⁹ × 16³ = 16⁹⁺³ = 16¹²
---
## 🔹 Row 4:
10.
4⁵ × 4⁶ = 4⁵⁺⁶ = 4¹¹
11.
10⁶ × 10⁸ = 10⁶⁺⁸ = 10¹⁴
12.
1¹ × 1⁵ = 1¹⁺⁵ = 1⁶
*(Note: 1 to any power is always 1, so 1⁶ = 1, but we write it as 1⁶ per instructions.)*
---
## 🔹 Row 5:
13.
14³ × 14² = 14³⁺² = 14⁵
14.
30²⁰ × 30⁵ = 30²⁰⁺⁵ = 30²⁵
15.
3⁹ × 3⁵ = 3⁹⁺⁵ = 3¹⁴
---
## 🔹 Row 6:
16.
7¹¹ × 7⁸ = 7¹¹⁺⁸ = 7¹⁹
17.
5⁷ × 5³ = 5⁷⁺³ = 5¹⁰
18.
8¹⁴ × 8⁹ = 8¹⁴⁺⁹ = 8²³
---
## 🔹 Row 7:
19.
11²⁰ × 11¹² = 11²⁰⁺¹² = 11³²
20.
7¹¹ × 7² = 7¹¹⁺² = 7¹³
21.
19⁴ × 19³ = 19⁴⁺³ = 19⁷
---
##
✔ Final Answers (All in single exponent form):
| Problem | Answer |
|---------|--------|
| 12¹⁴ × 12² |
12¹⁶ |
| 8⁵ × 8³ |
8⁸ |
| 13³ × 13³ |
13⁶ |
| 5⁸ × 5¹ |
5⁹ |
| 3⁸ × 3³ |
3¹¹ |
| 8¹⁵ × 8³ |
8¹⁸ |
| 6³ × 6² |
6⁵ |
| 2⁷ × 2² |
2⁹ |
| 16⁹ × 16³ |
16¹² |
| 4⁵ × 4⁶ |
4¹¹ |
| 10⁶ × 10⁸ |
10¹⁴ |
| 1¹ × 1⁵ |
1⁶ |
| 14³ × 14² |
14⁵ |
| 30²⁰ × 30⁵ |
30²⁵ |
| 3⁹ × 3⁵ |
3¹⁴ |
| 7¹¹ × 7⁸ |
7¹⁹ |
| 5⁷ × 5³ |
5¹⁰ |
| 8¹⁴ × 8⁹ |
8²³ |
| 11²⁰ × 11¹² |
11³² |
| 7¹¹ × 7² |
7¹³ |
| 19⁴ × 19³ |
19⁷ |
---
✔ Summary: Every problem uses the same simple rule —
add the exponents when bases are the same. No need to calculate the actual numbers; just combine the exponents!
Let me know if you want a printable answer key or explanations for specific problems!
Parent Tip: Review the logic above to help your child master the concept of product rule worksheet.
