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

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

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

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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.

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