Let's solve this step by step using the
Product Rule of Exponents.
🔷 Product Rule of Exponents:
When multiplying two powers with the
same base, you
add the exponents:
$$
a^m \times a^n = a^{m+n}
$$
We’ll apply this rule to each problem.
---
✔ Solutions:
1) $ 2^2 \times 2^2 = 2^{2+2} = \boxed{2^4} $
2) $ 6^4 \times 6^7 = 6^{4+7} = \boxed{6^{11}} $
3) $ 3^4 \times 3^3 = 3^{4+3} = \boxed{3^7} $
4) $ 12^2 \times 12^3 = 12^{2+3} = \boxed{12^5} $
5) $ 4^2 \times 4^4 = 4^{2+4} = \boxed{4^6} $
6) $ 2^8 \times 2^4 = 2^{8+4} = \boxed{2^{12}} $
7) $ 3^3 \times 3^5 = 3^{3+5} = \boxed{3^8} $
8) $ 5^6 \times 5^7 = 5^{6+7} = \boxed{5^{13}} $
9) $ 2^3 \times 2^3 = 2^{3+3} = \boxed{2^6} $
10) $ 10^7 \times 10^7 = 10^{7+7} = \boxed{10^{14}} $
11) $ 5^5 \times 5^6 = 5^{5+6} = \boxed{5^{11}} $
12) $ 3^5 \times 3^4 = 3^{5+4} = \boxed{3^9} $
13) $ 7^3 \times 7^3 = 7^{3+3} = \boxed{7^6} $
14) $ 9^2 \times 9^6 = 9^{2+6} = \boxed{9^8} $
15) $ 6^2 \times 6^3 = 6^{2+3} = \boxed{6^5} $
16) $ 8^4 \times 8^6 = 8^{4+6} = \boxed{8^{10}} $
17) $ 2^5 \times 2^3 = 2^{5+3} = \boxed{2^8} $
18) $ 5^8 \times 5^3 = 5^{8+3} = \boxed{5^{11}} $
19) $ 3^3 \times 3^4 = 3^{3+4} = \boxed{3^7} $
20) $ 2^5 \times 2^3 = 2^{5+3} = \boxed{2^8} $
---
✔ Final Answer Key:
| Problem | Answer |
|--------|--------------|
| 1 | $ 2^4 $ |
| 2 | $ 6^{11} $ |
| 3 | $ 3^7 $ |
| 4 | $ 12^5 $ |
| 5 | $ 4^6 $ |
| 6 | $ 2^{12} $ |
| 7 | $ 3^8 $ |
| 8 | $ 5^{13} $ |
| 9 | $ 2^6 $ |
| 10 | $ 10^{14} $ |
| 11 | $ 5^{11} $ |
| 12 | $ 3^9 $ |
| 13 | $ 7^6 $ |
| 14 | $ 9^8 $ |
| 15 | $ 6^5 $ |
| 16 | $ 8^{10} $ |
| 17 | $ 2^8 $ |
| 18 | $ 5^{11} $ |
| 19 | $ 3^7 $ |
| 20 | $ 2^8 $ |
>
✔ All answers follow the
product rule:
same base → add exponents.
Let me know if you'd like these evaluated as actual numbers!
Parent Tip: Review the logic above to help your child master the concept of basic exponent rules worksheet.
