Question
Question Simplify to a single power of 6: \[ \frac{6^{7}}{6^{3}} \] Answer Attempt 2 out of 2 Answer: \( 6 \square \) Submit Answer
Ask by Chang Lindsey. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(6^{4}\)
Solution
To simplify \(\frac{6^{7}}{6^{3}}\) to a single power of 6, you can use the **laws of exponents**, specifically the **quotient rule**, which states:
\[
\frac{a^{m}}{a^{n}} = a^{m-n}
\]
Applying this rule to your expression:
\[
\frac{6^{7}}{6^{3}} = 6^{7-3} = 6^{4}
\]
**Final Answer:** \(6^{4}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
When you're working with powers that have the same base, you simply subtract the exponents. So, in this case, you take \(7 - 3\) which gives you \(4\). Thus, \(\frac{6^7}{6^3}\) simplifies to \(6^4\). If you're ever confused about how to handle powers, remember that division in exponents means you can just knock off some of the top-level power! It's like giving a high-five and taking back three fingers—you're left with four fingers raised in the air, just like in \(6^4\)!
