Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![The image displays a mathematical expression that needs to be simplified. The problem is presented as follows:
"Simplify the given expression. Present your answer."
\[
\left(\frac{-3p^8q^2r^7}{15p^5q^2r^5}\right)^3 = \, \underline{\hspace{2cm}}
\]
There are options below the expression:
- Add Work
- Next Question
This is a complex fraction raised to the third power. To simplify it, follow these steps:
1. Simplify the fraction before raising it to the power:
- Simplify the coefficients: \(-3\) and \(15\) reduce to \(-\frac{1}{5}\).
- Simplify the powers of \(p\): \(p^8\) divided by \(p^5\) equals \(p^{8-5} = p^3\).
- Simplify the powers of \(q\): \(q^2\) divided by \(q^2\) equals \(q^{2-2} = q^0 = 1\).
- Simplify the powers of \(r\): \(r^7\) divided by \(r^5\) equals \(r^{7-5} = r^2\).
The simplified expression inside the parentheses is:
\[
\left(\frac{-1p^3r^2}{5}\right)^3
\]
2. Raise each part of the expression to the third power:
- \(\left(-\frac{1}{5}\right)^3 = -\frac{1}{125}\)
- \((p^3)^3 = p^9\)
- \((r^2)^3 = r^6\)
3. Combine these results:
\[
-\frac{p^9r^6}{125}
\]
This expression should be entered into the provided box next to the original equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb35c127b-5860-4a78-8624-93c14bbdfb80%2Fc7409149-8f37-4c81-83e3-2306cb9e88cd%2F4vydc89_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a mathematical expression that needs to be simplified. The problem is presented as follows:
"Simplify the given expression. Present your answer."
\[
\left(\frac{-3p^8q^2r^7}{15p^5q^2r^5}\right)^3 = \, \underline{\hspace{2cm}}
\]
There are options below the expression:
- Add Work
- Next Question
This is a complex fraction raised to the third power. To simplify it, follow these steps:
1. Simplify the fraction before raising it to the power:
- Simplify the coefficients: \(-3\) and \(15\) reduce to \(-\frac{1}{5}\).
- Simplify the powers of \(p\): \(p^8\) divided by \(p^5\) equals \(p^{8-5} = p^3\).
- Simplify the powers of \(q\): \(q^2\) divided by \(q^2\) equals \(q^{2-2} = q^0 = 1\).
- Simplify the powers of \(r\): \(r^7\) divided by \(r^5\) equals \(r^{7-5} = r^2\).
The simplified expression inside the parentheses is:
\[
\left(\frac{-1p^3r^2}{5}\right)^3
\]
2. Raise each part of the expression to the third power:
- \(\left(-\frac{1}{5}\right)^3 = -\frac{1}{125}\)
- \((p^3)^3 = p^9\)
- \((r^2)^3 = r^6\)
3. Combine these results:
\[
-\frac{p^9r^6}{125}
\]
This expression should be entered into the provided box next to the original equation.
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