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
Transcribed Image Text:The image presents a multiple-choice question related to algebraic expressions involving square roots. It is likely part of a problem set for practicing simplification or manipulation of radical expressions. The options are presented in standard format, with a circle to the left for selecting the correct answer. The choices given are:
1. \(\frac{1}{\sqrt{3x}}\)
2. \(\sqrt{(3x)^2}\)
3. \(\sqrt{3x}\)
4. \(\frac{1}{\sqrt{(3x)^2}}\)
Each option is placed next to a circular selection marker, allowing students to choose one as their answer.
There are no graphs or diagrams in this image. This question helps assess the students' ability to simplify or rewrite expressions involving square roots and exponents.
![### Question:
Select the expression that is equivalent to \((3x)^{-\frac{1}{2}}\)
### Explanation:
The goal of this problem is to identify an equivalent mathematical expression for the given expression \((3x)^{-\frac{1}{2}}\). To solve this, recall the properties of exponents:
1. \((a^m)^n = a^{m \cdot n}\)
2. \(a^{-n} = \frac{1}{a^n}\)
3. \(a^\frac{m}{n} = \sqrt[n]{a^m}\)
Using these rules, you start by expressing the given exponent in different forms:
- The negative exponent indicates a reciprocal: \((3x)^{-\frac{1}{2}} = \frac{1}{(3x)^{\frac{1}{2}}}\).
- The fractional exponent indicates a root: \((3x)^{\frac{1}{2}} = \sqrt{3x}\).
Thus:
- \((3x)^{-\frac{1}{2}} = \frac{1}{\sqrt{3x}}\).
So, \(\frac{1}{\sqrt{3x}}\) is an equivalent expression to \((3x)^{-\frac{1}{2}}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5f9c756-5bb5-4fec-8512-230ca00319ed%2F86c7d67c-5e50-414c-adaf-87c0a19ed780%2F5m5xadf_processed.png&w=3840&q=75)
Transcribed Image Text:### Question:
Select the expression that is equivalent to \((3x)^{-\frac{1}{2}}\)
### Explanation:
The goal of this problem is to identify an equivalent mathematical expression for the given expression \((3x)^{-\frac{1}{2}}\). To solve this, recall the properties of exponents:
1. \((a^m)^n = a^{m \cdot n}\)
2. \(a^{-n} = \frac{1}{a^n}\)
3. \(a^\frac{m}{n} = \sqrt[n]{a^m}\)
Using these rules, you start by expressing the given exponent in different forms:
- The negative exponent indicates a reciprocal: \((3x)^{-\frac{1}{2}} = \frac{1}{(3x)^{\frac{1}{2}}}\).
- The fractional exponent indicates a root: \((3x)^{\frac{1}{2}} = \sqrt{3x}\).
Thus:
- \((3x)^{-\frac{1}{2}} = \frac{1}{\sqrt{3x}}\).
So, \(\frac{1}{\sqrt{3x}}\) is an equivalent expression to \((3x)^{-\frac{1}{2}}\).
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