/*! 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 121 Describe what it means to raise ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 121

Describe what it means to raise a number to a power. In your description, include a discussion of the difference between \(-5^{2}\) and \((-5)^{2}\)

Short Answer

Expert verified
Raising a number to a power means multiplying the number by itself the specified number of times. The expressions \(-5^{2}\) and \((-5)^{2}\) are not the same. The first, \(-5^{2}\), results in \(-25\) and the second one, \((-5)^{2}\), results in \(+25\). The difference lies in whether the negative sign is included in the exponentiation.

Step by step solution

01

Understanding what it means to raise a number to a power

Raising a number to a power, also known as exponentiation, is a mathematical operation that multiplies a number (the base) by itself a specified number of times (the exponent). For example, \(3^{2}\) is equal to \(3*3 = 9\). This means the number 3 (base) is multiplied by itself for 2 (exponent) times.
02

Understanding the notation of \(-5^{2}\)

The expression \(-5^{2}\) denotes that the power of 2 applies only to the 5 and not to the negative sign. So, \(-5^{2}\) calculates as \(-(5 * 5) = -25\) as the negative sign here stands without alteration.
03

Interpretation of \((-5)^{2}\)

On the contrary, \((-5)^{2}\) means that the number -5 (which includes the negative sign) is being squared. Thus, it is \(-5*-5 = 25\). The negative number multiplied by negative gives a positive result, therefore the result is +25.
04

Comparing \(-5^{2}\) and \((-5)^{2}\)

From the above steps, it is observed that \(-5^{2}\) and \((-5)^{2}\) are not the same. The former results in \(-25\) as it squares only the 5, leaving the negative sign intact, while the latter results in \(+25\) since it squares the entire -5, including the negative sign.

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

Factor and simplify each algebraic expression. $$4 x^{-\frac{1}{3}}+8 x^{\frac{1}{3}}$$

Describe the kinds of numbers that have rational fifth roots.

What difference is there in simplifying \(\sqrt[3]{(-5)^{3}}\) and \(\sqrt[4]{(-5)^{4} ?}\)

Determine whether each statementmakes sense or does not make sense, and explain your reasoning. You grouped the polynomial鈥檚 terms using different groupingsthan I did, yet we both obtained the same factorization.

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{\frac{1}{2}} y^{-\frac{7}{4}}}{y^{-\frac{5}{4}}}\right)^{-4} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.