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Use the Product Rule of Exponents to simplify the expression \( 13^{10} \cdot 13^{4} \cdot \) (1 point) \( 13^{40} \) \( 169^{40} \) \( 13^{14} \) \( 169^{14} \) Check answer Remaining Attempts: 3

Ask by Bernard Barber. in the United States
Feb 11,2025

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Answer

The simplified expression is \( 13^{14} \).

Solution

The Product Rule of Exponents states that a^m * a^n = a^(m+n). Here we have: 13^10 * 13^4 = 13^(10 + 4) = 13^14. So, the simplified expression is 13^(14).

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Beyond the Answer

When you're multiplying exponents with the same base, you can simply add the exponents together. In this case, you have \( 13^{10} \cdot 13^{4} \). If you add the exponents, \( 10 + 4 = 14 \), which means the expression simplifies to \( 13^{14} \). So the correct answer is \( 13^{14} \)! Now, just a little tip: remember, the Product Rule of Exponents is not just for two exponents—feel free to apply it to as many terms as you like! For instance, \( a^m \cdot a^n \cdot a^p = a^{m+n+p} \)! If you're ever unsure, don't hesitate to revisit the basics. The exponents' rules are foundational and will serve you well in more complex algebraic manipulations!

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