/*! 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 49 Evaluate the given expression fo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 49

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$x y^{2}$$

Short Answer

Expert verified
The value of the expression for \(x = 2, y = -3\) is 18.

Step by step solution

01

Identify the given values

Identify the values provided in the problem. Here, we have: \( x = 2 \) \( y = -3 \) \( z = -4 \)
02

Substitute the values into the expression

Substitute the given values into the expression \(xy^{2}\). We replace \(x\) with 2 and \(y\) with -3.
03

Calculate \(y^{2}\)

First, solve for \(y^{2}\). Substitute \(y = -3 \) into the expression to get: \[ (-3)^{2} = 9 \]
04

Multiply the results

Now multiply the value of \(x\) by the result from Step 3: \(2 \times 9 = 18\)

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 Method
The substitution method is a way to simplify difficult mathematical expressions by replacing variables with given values. For example, in the exercise provided, the values of the variables are:
  • \tx = 2
  • \ty = -3
  • \tz = -4
To evaluate the expression \(xy^{2}\), we start by substituting the variables with these specific values.
Therefore, we replace \(x\) with 2 and \(y\) with -3. This is the first step in understanding and solving the expression effectively.
Exponents
Exponents are used to express repeated multiplication of a number by itself. In the given expression \(xy^{2}\), the exponent is 2, which means we need to multiply \( y \) by itself.
Therefore, \( y^2 = (-3)^2 \). To solve this:
  • First, understand that the base \(y\) is -3 and the exponent tells us to multiply -3 by itself.
  • Next, calculate \( (-3) \times (-3) \). A negative multiplied by a negative results in a positive number.
Thus,\[ (-3) \times (-3) = 9 \]This exponentiation step transforms the expression into something simpler for further calculations.
Multiplication
Multiplication is one of the fundamental arithmetic operations, involving the combination of two numbers to get a product. After calculating the exponent in the previous step, we arrive at 9.
Finally, we need to multiply this result by the given value of \( x \.\)
  • The given value of \( x \) is 2.
  • The result from the exponentiation step is 9.
Thus, we perform the multiplication:
\( 2 \times 9 = 18 \)Remember, understanding each operation individually makes evaluating expressions much easier. This step-by-step approach helps you solve the value of any given mathematical expression efficiently.

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

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$x y^{2}-(x y)^{2}$$

Evaluate the given expression for \(x=0.24\) and \(y=-0.5 .\) Round off to the nearest thousandth where necessary. $$\frac{10}{x}+\frac{8}{y}$$

Simplify by combining like terms whenever possible. $$7 y^{2}(y+2)+2 y\left(5 y^{2}\right)$$

Evaluate each expression. Round off your answer to the nearest thousandth where necessary. $$(3.81)^{3}-(2.64)^{2}$$

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$x-y+z$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.