Question

Evaluate expression. $(-125)^{1 / 3}$

   Evaluate expression.
$(-125)^{1 / 3}$

Algebra for College Students

Algebra for College Students

Mark Dugopolski 5th Edition

Chapter 7, Problem 17

Instant Answer

Solved by Expert Jeyasree R T

04/21/2020

Step 1

This can be written as the cube root of -125. Show more…

Show all steps

lock

Thanks for your feedback!

Evaluate expression. $(-125)^{1 / 3}$

Play audio

Feedback

Powered by NumerAI

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Fractional Exponents

Fractional exponents are a way of expressing both exponentiation and root extraction simultaneously. When a number is raised to an exponent of the form 1/n, this is equivalent to taking the nth root of that number. This concept is a cornerstone in algebra and helps in rewriting and simplifying expressions involving roots.

Cube Roots and Odd-Numbered Roots

Cube roots, or more generally odd-numbered roots, have the property that they can be applied to negative numbers with the result also being negative. Unlike even-numbered roots, which are not defined for negative numbers in the real number system, cube roots of negative numbers follow consistent arithmetic rules and are crucial for solving expressions involving negative bases.

Properties of Exponents

The properties of exponents, including the conversion between exponential and radical forms, form the basis for simplifying and evaluating expressions. Understanding these properties enables one to systematically and accurately manipulate algebraic expressions, ensuring correct evaluations even when dealing with negative numbers and fractional exponents.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later