Question
3 Find the quotient. Write your answer using exponents. \( \frac{7^{20}}{7^{4}} \)
Ask by Ramirez Kelly. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 7^{16} \)
Solution
**Step 1:**
Write the quotient of powers with the same base using the formula:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
**Step 2:**
Substitute in the given values where \( a = 7 \), \( m = 20 \), and \( n = 4 \):
\[
\frac{7^{20}}{7^4} = 7^{20-4}
\]
**Step 3:**
Simplify the exponent subtraction:
\[
7^{20-4} = 7^{16}
\]
**Answer:**
\[
7^{16}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
When you divide two numbers with the same base, you subtract the exponents. In this case, we have \( 7^{20} \div 7^{4} \). So, \( 20 - 4 = 16 \). Therefore, the answer is \( 7^{16} \). This neat little rule is super handy and can make working with large numbers a whole lot simpler! Now, instead of dealing with \( 7^{20} \) and \( 7^{4} \), you can focus on just the exponent, which is a much smaller number to handle and understand.
