Question
Simplify to a single power of 3 : \( 3^{6} \cdot 3^{5} \)
Ask by Simmons Campbell. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 3^{11} \)
Solution
1. Recognize the rule for multiplying powers with the same base:
\[
a^m \cdot a^n = a^{m+n}
\]
2. Apply the rule to the expression \(3^6 \cdot 3^5\):
\[
3^6 \cdot 3^5 = 3^{6+5}
\]
3. Simplify the exponent:
\[
6+5 = 11
\]
4. Write the final simplified expression:
\[
3^{11}
\]
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Simplify this solution Mind Expander
To simplify \( 3^{6} \cdot 3^{5} \), you can use the property of exponents that states \( a^{m} \cdot a^{n} = a^{m+n} \). Here, you add the exponents: \( 6 + 5 = 11 \). So, \( 3^{6} \cdot 3^{5} = 3^{11} \). And there you have it—the simplified expression is \( 3^{11} \)!
