Question
5 Find the quotient. Write your answer using exponents. \( \frac{x^{9}}{x^{4}} \)
Ask by Cervantes West. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The quotient is \( x^{5} \).
Solution
1. Start with the division of exponential expressions:
\[
\frac{x^{9}}{x^{4}}
\]
2. Use the law of exponents which states:
\[
\frac{x^a}{x^b} = x^{\,a-b}
\]
where \(a = 9\) and \(b = 4\).
3. Subtract the exponents:
\[
x^{9-4} = x^{5}
\]
Thus, the quotient is \( x^{5} \).
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Simplify this solution Bonus Knowledge
When dividing exponential expressions with the same base, you subtract the exponents. So for \( \frac{x^{9}}{x^{4}} \), you calculate \( 9 - 4 \), which gives you \( x^{5} \). Thus, the quotient is \( x^{5} \). Now, remember that whatever you do to the exponents follows the laws of exponents! So keep that in mind for future division! If you have extra practice with more complex exponents, it can become a fun challenge to test your skills!
