/*! 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 2 Explain how to write \(1^{1 / 3}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 2

Explain how to write \(1^{1 / 3}\) in radical form.

Short Answer

Expert verified
The expression \(1^{1/3}\) can be written in radical form by converting the fractional exponent to a radical. The denominator of the exponent, \(3\), represents the root, and the numerator, \(1\), represents the power. So, the expression can be written as \(\sqrt[3]{1}\). Since the cube root of any number to the power of \(1\) is equal to the base number itself, \(\sqrt[3]{1}\) simplifies to \(1\).

Step by step solution

01

Understand the expression

The expression we are working with is \(1^{1/3}\). Here, the base is \(1\), and the exponent is a fraction \(\frac{1}{3}\). We need to convert this expression into a radical form, which involves finding the root of the base.
02

Convert the exponent into a radical

Recall that when writing a fractional exponent, the numerator represents the power, and the denominator represents the root. In this case, the power is \(1\) and the root is \(3\). Therefore, we can convert the fractional exponent \(\frac{1}{3}\) into a radical form: \(\sqrt[3]{1}\), where the base is \(1\).
03

Simplify the expression if possible

In this case, the expression \(\sqrt[3]{1}\) can be simplified, since the cube root of any number to the power of \(1\) is equal to the base number itself. Therefore, \(\sqrt[3]{1} = 1\). So, the radical form of \(1^{1/3}\) is \(\sqrt[3]{1}\), which can be simplified to \(1\).

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

Rationalize the denominator and simplify completely. Assume the variables represent positive real numbers. $$\frac{\sqrt{32}}{\sqrt{5}-\sqrt{7}}$$

Perform the indicated operation and simplify. Assume all variables represent positive real numbers. $$\frac{\sqrt{72 c^{10}}}{\sqrt{6 c^{2}}}$$

Find the conjugate of each binomial. Then, multiply the binomial by its conjugate. $$(\sqrt{5}-4)$$

Fill in the blank. Assume all variables represent positive real numbers. $$\sqrt[5]{4} \cdot \sqrt[5]{7}=\sqrt[5]{2^{5}}=2$$

Rationalize the denominator and simplify completely. Assume the variables represent positive real numbers. $$\frac{\sqrt{u}}{\sqrt{u}-\sqrt{v}}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

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.