Question
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Tutor-Verified Answer
Answer
\( 3^{6} \times 3 = 2187 \)
Solution
1. Recognize that \( 3 = 3^1 \), so the expression becomes
\[
3^6 \times 3^1.
\]
2. Use the exponent property: when multiplying powers with the same base, add the exponents:
\[
3^6 \times 3^1 = 3^{6+1} = 3^7.
\]
3. Calculate \( 3^7 \):
\[
3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187.
\]
The final answer is \( 2187 \).
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Simplify this solution The Deep Dive
Did you know that multiplying powers with the same base is as easy as adding their exponents? That's right! In this case, you have \( 3^{6} \times 3^{1} \), which means you can simply add the exponents: \( 6 + 1 = 7 \). So, the expression simplifies to \( 3^{7} \). Now, if you're curious about the value of \( 3^{7} \), it's equal to 2187! This number may not come up in everyday life, but it's fascinating to see how exponential growth works, especially when you consider how quickly numbers can escalate just by raising them to higher powers!
