Potter Reese
01/28/2024 · High School
(8) \( \left(\frac{x^{-3}}{y^{-5}}\right)^{-3}:\left(\frac{x}{y^{3}}\right)^{7} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( \left(\frac{x^{-3}}{y^{-5}}\right)^{-3}:\left(\frac{x}{y^{3}}\right)^{7} \), we will handle each part step by step.
1. **Simplify the first part**: \( \left(\frac{x^{-3}}{y^{-5}}\right)^{-3} \)
Using the property of exponents \( (a/b)^{-n} = \frac{b^n}{a^n} \), we have:
\[
\left(\frac{x^{-3}}{y^{-5}}\right)^{-3} = \frac{(y^{-5})^{-3}}{(x^{-3})^{-3}} = \frac{y^{15}}{x^{9}}
\]
2. **Simplify the second part**: \( \left(\frac{x}{y^{3}}\right)^{7} \)
Again using the property of exponents:
\[
\left(\frac{x}{y^{3}}\right)^{7} = \frac{x^{7}}{(y^{3})^{7}} = \frac{x^{7}}{y^{21}}
\]
3. **Combine the two parts**: Now we need to divide the two results:
\[
\frac{y^{15}}{x^{9}} : \frac{x^{7}}{y^{21}} = \frac{y^{15}}{x^{9}} \cdot \frac{y^{21}}{x^{7}} = \frac{y^{15} \cdot y^{21}}{x^{9} \cdot x^{7}} = \frac{y^{36}}{x^{16}}
\]
Thus, the simplified expression is:
\[
\frac{y^{36}}{x^{16}}
\]
Quick Answer
The simplified expression is \( \frac{y^{36}}{x^{16}} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit