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Chapter 5: Problem 62

For Exercises \(59-66,\) simplify the expressions. $$(-2.4)^{2}$$

Short Answer

Expert verified
5.76

Step by step solution

01

Identify the Expression

The expression given to simplify is \( (-2.4)^2 \).
02

Understand Exponents

The exponent indicates that the base (in this case, -2.4) should be multiplied by itself. So here, \( (-2.4)^2 = (-2.4) \times (-2.4) \).
03

Multiply the Numbers

Calculate the product of -2.4 and -2.4: \( (-2.4) \times (-2.4) = 5.76 \).
04

Simplify the Result

The simplified result of the expression \( (-2.4)^2 \) is \ 5.76 \.

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Key Concepts

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

Understanding Exponents
An exponent, sometimes called a power, tells you how many times to use a number in a multiplication. If you have a term like \(a^n\), \(a\) is the base, and \(n\) is the exponent. For example, in \((-2.4)^2\), \(-2.4\) is the base, and \(2\) is the exponent. This means you multiply \(-2.4\) by itself. Written out, it looks like this: \((-2.4) \times (-2.4)\). The exponent \(2\) here tells us to repeat the base once.
Negative Numbers and Exponents
Negative numbers can sometimes confuse people when combined with exponents. Here, we have \(-2.4\) raised to the power of \(2\). Remember, multiplying two negative numbers always gives a positive result: \((-2) \times (-2) = 4\). Applying this to our example, \((-2.4) \times (-2.4) = 5.76\). When the exponent is even, the result will be positive. If the exponent had been odd, the product would remain negative.
Simplifying with Multiplication
To simplify expressions with exponents, you often need to perform multiplication. Here鈥檚 a recap of our example expression \((-2.4)^2\). Breaking it down: \((-2.4) \times (-2.4)\). First, multiply the absolute values: \2.4 \times 2.4 = 5.76\. Next, check the signs: a negative times a negative is positive. Thus, the final result is \5.76\. Multiplication helps combine numbers, and understanding the rules for negative signs is crucial in getting the right answer.

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Most popular questions from this chapter

For Exercises \(71-82,\) simplify by using the order of operations. $$63.75-9.5(4)$$

Which number properly represents 3.499999 rounded to the thousandths place? a. 3.500 b. 3.5 c. 3.500000 d. 3.499

For Exercises \(59-66,\) simplify the expressions. $$(-1.3)^{2}$$

For Exercises \(71-82,\) simplify by using the order of operations. $$15.06-1.92-0.4^{2}$$

For Exercises \(85-90,\) refer to the table. The table gives the closing stock prices (in dollars per share) for the first day of trading for the given month. $$\begin{array}{l|c|c|c|c|c} \text { Stock } & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \\ \hline \text { IBM } & \$ 97.27 & \$ 99.00 & \$ 92.27 & \$ 95.21 & \$ 103.17 \\\ \hline \text { FedEx } & \$ 109.77 & \$ 111.89 & \$ 114.16 & \$ 106.07 & \$ 106.11 \\ \hline \end{array}$$ Between which two consecutive months did the IBM stock increase the most? What was the amount of increase?
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