/*! 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 142 Explain how to simplify \(\sqrt[... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 142

Explain how to simplify \(\sqrt[3]{x} \cdot \sqrt{x}\)

Short Answer

Expert verified
So, the simplified form of \(\sqrt[3]{x} \cdot \sqrt{x}\) is \(x^{5/6}\)

Step by step solution

01

Identify the structure of the expression

Firstly, identify the current structure of the expression: it is a multiplication of the cube root of x (\(x^{1/3}\)) and the square root of x (\(x^{1/2}\)).
02

Convert roots to fractional exponents

Next, transform these roots into their equivalent fractional exponents. This results in \((x^{1/3}) * (x^{1/2})\). Here, \(x^{1/3}\) represents the cube root of x, and \(x^{1/2}\) represents the square root of x.
03

Apply the rule of exponents for multiplication

Multiplication operation on the basis of the same number allows us to add the exponents. This results in \(x^{1/3 + 1/2}\).
04

Simplify the added fractional exponents

Adding 1/3 and 1/2 gives us 5/6. This results in \(x^{5/6}\).

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

In Exercises \(105-112,\) add or subtract as indicated. Begin by rationalizing denominators for all terms in which denominators contain radicals. $$\sqrt[3]{25}-\frac{15}{\sqrt[3]{5}}$$

In Exercises \(75-92,\) rationalize each denominator. Simplify, if possible. $$\frac{35}{5 \sqrt{2}-3 \sqrt{5}}$$

In Exercises \(105-112,\) add or subtract as indicated. Begin by rationalizing denominators for all terms in which denominators contain radicals. $$\sqrt{15}-\sqrt{\frac{5}{3}}+\sqrt{\frac{3}{5}}$$

Exercises \(147-149\) will help you prepare for the material covered in the first section of the next chapter. Solve by factoring: \(x^{2}=9\)

Factor: \(y^{2}-6 y+9-25 x^{2}\) (Section 6.5, Example 8)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Geometry

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.