Let’s solve each problem using the
Exponents Product Rule.
The rule is:
When you multiply two powers with the same base, you
add the exponents.
That means:
> \( a^m \times a^n = a^{m+n} \)
We’ll go row by row and apply this rule to every problem.
---
Row 1:
- \( 12^{14} \times 12^2 = 12^{14+2} = 12^{16} \)
- \( 8^5 \times 8^3 = 8^{5+3} = 8^8 \)
- \( 13^3 \times 13^3 = 13^{3+3} = 13^6 \)
---
Row 2:
- \( 5^8 \times 5^1 = 5^{8+1} = 5^9 \)
- \( 3^8 \times 3^3 = 3^{8+3} = 3^{11} \)
- \( 8^{15} \times 8^3 = 8^{15+3} = 8^{18} \)
---
Row 3:
- \( 6^3 \times 6^2 = 6^{3+2} = 6^5 \)
- \( 2^7 \times 2^2 = 2^{7+2} = 2^9 \)
- \( 16^9 \times 16^3 = 16^{9+3} = 16^{12} \)
---
Row 4:
- \( 4^5 \times 4^6 = 4^{5+6} = 4^{11} \)
- \( 10^6 \times 10^8 = 10^{6+8} = 10^{14} \)
- \( 1^1 \times 1^5 = 1^{1+5} = 1^6 \) → (Note: 1 to any power is still 1, but we write it as \(1^6\) per instructions.)
---
Row 5:
- \( 14^3 \times 14^2 = 14^{3+2} = 14^5 \)
- \( 30^{20} \times 30^5 = 30^{20+5} = 30^{25} \)
- \( 3^9 \times 3^5 = 3^{9+5} = 3^{14} \)
---
Row 6:
- \( 7^{11} \times 7^8 = 7^{11+8} = 7^{19} \)
- \( 5^7 \times 5^3 = 5^{7+3} = 5^{10} \)
- \( 8^{14} \times 8^9 = 8^{14+9} = 8^{23} \)
---
Row 7:
- \( 11^{20} \times 11^{12} = 11^{20+12} = 11^{32} \)
- \( 7^{11} \times 7^2 = 7^{11+2} = 7^{13} \)
- \( 19^4 \times 19^3 = 19^{4+3} = 19^7 \)
---
All problems solved correctly by adding exponents when bases are the same.
Final Answer:
12¹⁶, 8⁸, 13⁶, 5⁹, 3¹¹, 8¹⁸, 6⁵, 2⁹, 16¹², 4¹¹, 10¹⁴, 1⁶, 14⁵, 30²⁵, 3¹⁴, 7¹⁹, 5¹⁰, 8²³, 11³², 7¹³, 19⁷
Parent Tip: Review the logic above to help your child master the concept of exponent product rule worksheet.
