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31 Ovr Qv(31)2 O (3x)²

31 Ovr Qv(31)2 O (3x)²

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter44: Solution Of Equations By The Subtraction, Addition, And Division Principles Of Equality
Section: Chapter Questions
Problem 2A: Use scientific notation to solve (6.325 108)(9.4 109)5105 . Leave the answer in scientific notation...
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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.
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 \((3x)^{-\frac{1}{2}}\).
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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