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Chapter 8: Problem 40

Evaluate the given expression for \(x=-3\) and \(y=5\) $$x y^{2}$$

Short Answer

Expert verified
The value of the expression is \(-75\).

Step by step solution

01

Substitute the values of x and y

Substitute the given values into the expression. Here, the values are \(x = -3\) and \(y = 5\). So the expression \(x y^{2}\) becomes \((-3) \times (5)^{2}\).
02

Calculate the square of y

Compute the square of the value of \(y\). That is \(5^{2}\). Calculating this gives: \(5^{2} = 25\).
03

Multiply x by the result

Now, multiply \(x\) by the result from Step 2. This means multiplying \(-3\) by \(25\). Thus, the expression \((-3) \times 25\) equals \(-75\).

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Key Concepts

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

substitution in algebra
Substitution in algebra is a fundamental concept that helps evaluate expressions by replacing variables with given values. It's like solving a puzzle where you know some pieces and fit them into the correct places. For example, in the given expression, we substitute \(x\) with \(-3\) and \(y\) with \(5\).
After substitution, our expression looks like this: \((-3) \times (5)^{2}\). By doing this, we simplify our problem into something that can be easily computed.
exponentiation
Exponentiation is the process of raising one number (the base) to the power of another number (the exponent). Here, in the expression \((-3) \times (5)^{2}\), we have an exponentiation step: \((5)^{2}\).
This means we multiply 5 by itself, giving us: \(5 \times 5 = 25\). It's important to always handle the exponentiation before moving onto multiplication, as per the order of operations rules.
multiplication of integers
The final step requires us to multiply the result of the exponentiation by the substituted value of \(x\). Multiplication of integers can have different outcomes, depending on the signs of the numbers involved:
  • If both numbers are positive or both are negative, the result is positive.
  • If one number is positive and the other is negative, the result is negative.
In this exercise, we multiply \(-3\) by 25.
Since one number is negative and the other is positive, the result is negative: \((-3) \times 25 = -75\).

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Most popular questions from this chapter

Perform the indicated operations and simplify. $$\left(5 x^{2} y\right)^{2}$$

Factor each of the following expressions as completely as possible. If an expression is not factorable, say so. $$t^{2}-1$$

Evaluate the given expression for \(x=-3\) and \(y=5\) $$(x y)^{2}$$

Divide each of the following. Use the long division process where necessary. $$\frac{2 x^{3}-3 x^{2}-x+12}{2 x+3}$$

Divide each of the following. Use the long division process where necessary. $$\frac{y^{3}+y^{2}+y-14}{y-2}$$
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