/*! 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 65 evaluate the given expression fo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 65

evaluate the given expression for \(w=2, x=-3, y=4,\) and \(z=-5\) $$\frac{-w^{2}}{(-w)^{2}}$$

Short Answer

Expert verified
-1

Step by step solution

01

Substitute Values

Replace the variable \( w \) with its given value, which is 2. The expression becomes: \( \frac{-(2)^{2}}{(-(2))^{2}} \).
02

Calculate the Numerator

Calculate \( -(2)^{2} \). First, find \( 2^2 \): \( 2^2 = 4 \). Then, apply the negative sign: \( -(4) = -4 \). So, the numerator is \( -4 \).
03

Calculate the Denominator

Calculate \( (-(2))^{2} \). First, find \( -(2) \), which is \( -2 \). Then, square \( -2 \): \( (-2)^2 \): \( -2 \times -2 = 4 \). So, the denominator is \( 4 \).
04

Divide the Numerator by the Denominator

Divide the calculated numerator by the calculated denominator: \( \frac{-4}{4} = -1 \).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution
Substitution involves replacing variables with their given numerical values to simplify and evaluate expressions. In our example, we replaced the variable \(w\) with 2. This helps in transforming the original expression \(\frac{-w^2}{(-w)^2}\) into \(\frac{-(2)^2}{(-(2))^2}\). Always ensure to substitute the exact values as provided.

For example, if you had \(x = -3\), you would substitute \(x\) with -3 in any part of an expression involving \(x\). Substitution is the first step in solving or simplifying algebraic expressions because it turns the expression from abstract to concrete.
Exponents
Exponents represent repeated multiplication of a number by itself. In our example, the expression contains \(\frac{-(2)^2}{(-(2))^2}\). Let's break this down:

1. **Numerator:** \(-(2)^2\), which means squaring 2 first (2 \cdot\ 2 = 4) and then applying the negative sign to get -4.
2. **Denominator:** \(-(2))^2\), which means first dealing with the negative sign to get -2, then squaring -2 (\(-2) \cdot \ (-2) = 4\).

Remember, the placement of the negative sign matters. In one case, you're squaring the positive number and then making it negative, while in the other, you're squaring a negative number which results in a positive outcome because two negatives make a positive.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. In the final step of our problem, we divided the numerator by the denominator:

1. **Numerator:** -4.
2. **Denominator:** 4.
3. Perform the division: \(\frac{-4}{4}\).

To do this, you simply divide -4 by 4, which results in -1. Division operations can be tricky when negative numbers are involved, but remember the basic rule: a negative divided by a positive yields a negative result. This is how arithmetic operations are applied after exponents and substitution have simplified the expression.

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

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(2 y+3)(y-5)$$

Estimate the answer without actually carrying out the computation and make the most appropriate choice. If you multiply \(1.93 \times 10^{5}\) by \(5.12 \times 10^{-3},\) the result is closest to (a) 10 (b) 1000 (c) \(10,000\) (d) 0.01 (e) 0.001

What can you say about the sign of the exponent of 10 of a number written in scientific notation if the number is bigger than \(1 ?\) If the number is smaller than \(1 ?\) Why?

Solve for x. $$5-2 x \geq 17$$

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(3 x+4)(5 x-7)$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

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.