/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 26 Convert to expressions with rati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 26

Convert to expressions with rational exponents. \(\frac{1}{\sqrt{m}}\)

Short Answer

Expert verified
The expression is \(m^{-\frac{1}{2}}\).

Step by step solution

01

Understanding the expression

Start with the given expression: \ \ \(\frac{1}{\sqrt{m}}\)
02

Identify the radical

In this expression, \(\sqrt{m}\) is a square root, which can be written with a rational exponent. Recall that the square root of a number is equal to raising that number to the power of \(\frac{1}{2}\). Therefore, \(\sqrt{m} = m^{\frac{1}{2}}\).
03

Rewrite the denominator

Rewrite the original expression by replacing the square root with its equivalent rational exponent: \ \ \(\frac{1}{m^{\frac{1}{2}}}\)
04

Apply the negative exponent rule

Using the negative exponent rule, which states that \(\frac{1}{a^b} = a^{-b}\), we can rewrite the expression as \ \ \(m^{-\frac{1}{2}}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

radical expressions
Radical expressions involve roots, such as square roots, cube roots, and more. In our exercise, we started with the expression \(\frac{1}{\sqrt{m}}\). Radicals can be converted to expressions with rational exponents. This makes calculations easier and often clearer. For example, the square root of a number \(m\) can be written as \(m^{\frac{1}{2}}\). This idea is key when simplifying or manipulating radical expressions. Understanding this relationship is helpful in algebra and higher math.
negative exponents
Negative exponents can appear confusing, but they follow simple rules. When you have an exponent that is negative, it indicates the reciprocal of the base raised to the positive version of that exponent. For example, \(a^{-b} = \frac{1}{a^b}\). In our exercise, we transformed \(\frac{1}{m^{\frac{1}{2}}}\) into \(m^{-\frac{1}{2}}\). This negative exponent rule helps simplify expressions and solve equations. Always remember, a negative exponent simply means 'one over' that base raised to the corresponding positive exponent.
square roots
Square roots are a specific type of radical. The square root of \(m\) is \(m^\frac{1}{2}\). In our exercise, we converted the square root into a rational exponent to simplify the expression. Square roots are common in many areas of math. Knowing that \(\sqrt{m} = m^{\frac{1}{2}}\) gives us flexibility in solving problems. It's a fundamental concept in algebra and calculus. Whenever you're dealing with square roots, think of them as exponents, which can make the math easier to handle.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use a calculator to find the values of the following trigonometric functions. \(\cos 12^{\circ}\)

For the following functions, find the amplitude, period, and mid-line. Also, find the maximum and minimum. $$ y=5 \cos (t / 2)+1 $$

Sound Waves. The pitch of a sound wave is measured by its frequency. Humans can hear sounds in the range from 20 to \(20,000 \mathrm{~Hz}\), while dogs can hear sounds as high as \(40,000 \mathrm{~Hz}\). The loudness of the sound is determined by the amplitude. \({ }^{22}\). The note A above middle \(C\) on a piano generates a sound modeled by the function \(g(t)=4 \sin (880 \pi t)\), where \(t\) is in seconds. Find the frequency of \(\mathrm{A}\) above middle \(\mathrm{C}\).

Use a calculator to find the degree measure of an acute angle whose trigonometric function is given. \(\sin t=0.87\)

At the apex of the basilar membrane, the fibers are long, flexible, and wide. At the apex, the basilar fibers are most affected by what kind of sound frequencies?
See all solutions

Recommended explanations on Biology Textbooks

Bioenergetics

Read Explanation

Heredity

Read Explanation

Chemistry of Life

Read Explanation

Microbiology

Read Explanation

Energy Transfers

Read Explanation

Biological Structures

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.