Open in App
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Chapter 7: Chapter 7

Problem 107

Next question

If \(a=3\) and \(b=2\), find \((6 a-b)^{-5 / 4}\)

Short Answer

Expert verified
\(\frac{1}{32}\)
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Try Premium for free

Over 22 million students worldwide already upgrade their learning with Vaia!

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Substitute the given values

We are given that \(a=3\) and \(b=2\). We start by substituting these values into the given expression \((6a-b)^{-5/4}\).

Step 2: Simplify the expression

After substituting values for \(a\) and \(b\), we get: \[(6(3)-2)^{-5/4}\] Now, simplifying the expression inside the parentheses: \[(18-2)^{-5/4}\] \[(16)^{-5/4}\]

Step 3: Evaluate the power

Now we need to evaluate the power with a negative exponent and a fraction. We can do this by breaking down the power into two parts. The \(-5/4\) power can be thought of as first raising the expression to the reciprocal of 4 and then raising to the power of -5. \[\left(16^{\frac{1}{4}}\right)^{-5}\] Now, \(16^{\frac{1}{4}}\) means the fourth root of 16, which is 2: \[(2)^{-5}\] Finally, we can evaluate the negative exponent. The power of -5 means finding the reciprocal: \[\frac{1}{2^5}\] And simplify the expression: \[\frac{1}{32}\] So the final answer is: \[(6a-b)^{-5 / 4} = \frac{1}{32}\]

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 7

Find the product by inspection: \(\sqrt{3}(\mathrm{x}-\sqrt{5})(\mathrm{x}+\sqrt{5})\).
Chapter 7

Find the value of \(3 x^{2}-4 x-2\), for \(x=(2-\sqrt{10}) / 3\).
Chapter 7

Evaluate \(16^{-3 / 4}\)
Chapter 7

Rationalize \(\quad 3 \sqrt{3 a x} /{ }^{3} \sqrt{4 a^{2}}\)
Chapter 7

Rationalize the denominator in the quotient: \(1 /(\sqrt{x}-\sqrt{y})\)
See all solutions

More chapters from the book ‘Algebra and Trigonometry’

See all chapters

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App
Create your free account now
Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Math

Pure Maths

Read Explanation
Math

Statistics

Read Explanation
Math

Probability and Statistics

Read Explanation
Math

Decision Maths

Read Explanation
Math

Calculus

Read Explanation
Math

Geometry

Read Explanation
View all explanations