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Chapter 8: Problem 41

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

Short Answer

Expert verified
225

Step by step solution

01

Substitute the values of x and y

First, substitute the given values of the variables into the expression. Here, the values are: \(x = -3\) and \(y = 5\). Thus, the expression \((x y)^{2}\) becomes \((-3 * 5)^{2}\).
02

Calculate the product inside the parenthesis

Next, calculate the product of \(-3\) and \(5\). This gives us \((-3) * 5 = -15\). So, the expression now is \((-15)^{2}\).
03

Square the result

Finally, square the result obtained in Step 2. Squaring \(-15\) gives us \((-15)^{2} = 225\).

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Key Concepts

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

substitution method
The substitution method is a technique used to evaluate algebraic expressions by replacing variables with given values. In our problem, we were given the variables \(x\) and \(y\) with values \(x = -3\) and \(y = 5\). The key steps in this method include:
  • Identifying the variables and their corresponding values.
  • Replacing each variable in the expression with its value.
By substituting \(x = -3\) and \(y = 5\) into the expression \((xy)^2\), we simplified the expression to \((-3 * 5)^2\).
algebraic expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. They do not have an equals sign. In our example, the expression \((xy)^2\) is an algebraic expression where \(x\) and \(y\) are variables. To evaluate such expressions:
  • First, substitute the given values of the variables.
  • Then, perform the arithmetic operations according to the order of operations.
In our problem, once we substituted \(x = -3\) and \(y = 5\), we multiplied these values to get \(-15\), and then squared the result to get \(225\).
exponentiation
Exponentiation is a mathematical operation that involves raising a number to the power of another number. In our example, we had to raise \(-15\) to the power of 2, denoted as \(-15^{2}\). The basic steps for exponentiation include:
  • Identifying the base (\(-15\) in our problem).
  • Identifying the exponent (2 in our problem).
  • Multiplying the base by itself as many times as indicated by the exponent.
So, \(-15 \times -15 = 225\). Squaring \(-15\) resulted in a positive number because a negative number times itself is positive.

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Most popular questions from this chapter

Factor each of the following expressions as completely as possible. If an expression is not factorable, say so. $$6 x^{2}-30 x+36$$

Factor each of the following expressions as completely as possible. If an expression is not factorable, say so. $$x^{2}+4 x$$

Solve each equation. Be sure to note whether the equation is quadratic or linear. $$9 y^{2}+4=12 y$$

Simplify the expression and express your final answer with positive exponents only. $$\left(x^{-3}\right)^{-4}$$

If a rocket is shot straight up into the air from ground level with an initial velocity of \(240 \mathrm{ft}\) per second, its height \(h\) (in feet) above the ground \(t\) seconds after it is launched is given by the equation \(h=240 t-16 t^{2} .\) How long does it take for the rocket to reach a height of 800 ft? Explain the significance of your answer(s).
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