/*! 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 90 Convert the expressions to radic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 90

Convert the expressions to radical form. $$ x^{-1 / 3} y^{3 / 2} $$

Short Answer

Expert verified
The expression in radical form is \(\sqrt[3]{x^{-1}} \sqrt{y^3}\).

Step by step solution

01

Identify the rational exponents

In the given expression, we have two rational exponents: -1/3 and 3/2.
02

Convert the rational exponents to radicals

To convert the rational exponent to a radical, use the following rule: \(a^{\frac{m}{n}} = \sqrt[n]{a^m}\). Apply this rule to both exponents: For \(x^{-1/3}\), we have: \[ x^{-\frac{1}{3}} = \sqrt[3]{x^{-1}} \] For \(y^{3/2}\), we have: \[ y^{\frac{3}{2}} = \sqrt[2]{y^3} \]
03

Combine the radicals

Now that we have both expressions in radical form, we can combine them into one expression: \[ x^{-\frac{1}{3}} y^{\frac{3}{2}} = \sqrt[3]{x^{-1}} \cdot \sqrt[2]{y^3} \] So, the expression in radical form is: \[ \sqrt[3]{x^{-1}} \sqrt{y^3} \]

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!

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

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(3^{\wedge} 2+2^{\wedge} 2+1\)

\(y^{4}+2 y^{2}-3\)

\(\left(x^{3}-2 x^{2}+4\right)\left(3 x^{2}-x+2\right)\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(2 x^{2}-5=0\)

\(x^{4}-5 x^{2}+4\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Decision Maths

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.