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Chapter 0: Problem 23

Simplify each exponential expression. $$x^{-2} y$$

Short Answer

Expert verified
The simplified form of the exponential expression \(x^{-2} y\) is \(\frac{y}{x^{2}}\).

Step by step solution

01

Identify the term with a negative exponent

In the given expression \(x^{-2} y\), the term with a negative exponent is \(x^{-2}\).
02

Apply the property of negative exponents

According to the property of negative exponents, a number to a negative exponent is equivalent to the reciprocal of that number to the positive exponent. Thus, \(x^{-2}\) can be written as \(\frac{1}{x^{2}}\).
03

Substitute the term with its equivalent form

Replace \(x^{-2}\) in the original expression \(x^{-2} y\) with its equivalent form \(\frac{1}{x^{2}}\) to get \(\frac{1}{x^{2}} y\) or \(\frac{y}{x^{2}}\).

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Most popular questions from this chapter

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. Parts for an automobile repair cost \(\$ 175 .\) The mechanic charges \(\$ 34\) per hour. If you receive an estimate for at least \(\$ 226\) and at most \(\$ 294\) for fixing the car. what is the time interval that the mechanic will be working on the job?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The model \(P=-0.18 n+2.1\) describes the number of pay phones, \(P,\) in millions, \(n\) years after \(2000,\) so I have to solve a linear equation to determine the number of pay phones in 2010.

What's wrong with this argument? Suppose \(x\) and \(y\) represent two real numbers, where \(x>y .\) $$\begin{aligned} &2>1\\\ &2(y-x)>1(y-x)\\\ &2 y-2 x>y-x\\\ &\begin{aligned} y-2 x &>-x \\ y &>x \end{aligned} \end{aligned}$$ The final inequality, \(y>x,\) is impossible because we were initially given \(x>y\)

Describe how to solve an absolute value inequality involving the symbol \(>.\) Give an example.

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3
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