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Chapter 0: Problem 17

Write each expression using exponents. $$ (0.8)(0.8) $$

Short Answer

Expert verified
(0.8)^2

Step by step solution

01

Understand Repeated Multiplication

Recognize that multiplication of the same number multiple times is equivalent to using an exponent.
02

Identify the Base

Identify the number being repeatedly multiplied. In this case, the number is 0.8.
03

Count the Number of Factors

Count how many times the number 0.8 is multiplied by itself. Here, it is multiplied twice.
04

Write with Exponents

Use the base and the count as the exponent to rewrite the expression. Since 0.8 is multiplied twice, the expression is converted to exponents as: y = (0.8)(0.8) = (0.8)^2

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Key Concepts

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

multiplication
Multiplication is a basic arithmetic operation where you combine equal groups. For example, if you have three baskets each with five apples, the total number of apples is 3 times 5, or 15 apples. In mathematical terms, multiplication is represented by an asterisk (*) or parentheses (). For instance, 2 multiplied by 3 can be written as (2)(3) or 2*3. This operation is foundational in understanding more complex concepts like exponents.
base number
The base number is the number that is being multiplied by itself in an expression using exponents. In the expression (0.8)^2, 0.8 is the base number. Recognizing the base is crucial because it tells us which number is repeatedly multiplied. The base number can be any real number, such as a decimal, fraction, or whole number. Understanding the base number helps in working through exponent problems effectively.
exponents
Exponents are a way to express repeated multiplication concisely. Instead of writing out a multiplication problem like (0.8)(0.8), we use an exponent to make it simpler: (0.8)^2. The exponent, in this case, 2, tells us how many times to multiply the base number, 0.8, by itself. Exponents make calculations easier and more manageable, especially with larger numbers or multiple repetitions. For example, (2^3) is equivalent to (2)(2)(2).
repeated multiplication
Repeated multiplication means multiplying the same number several times. For example, (0.8)(0.8)is a repeated multiplication of the number 0.8. Writing this using exponents saves time and space. So, (0.8)(0.8) becomes (0.8)^2. Understanding this concept is key for dealing with and simplifying expressions in mathematics, making it easier to work with larger sets of numbers and more complex equations.

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Most popular questions from this chapter

Problems like this one occasionally appear on social media. Simplify this expression. $$7+7 \div 7+7 \times 7-7$$

Simplify each expression. $$ 10-2^{2}+9-(1-8) $$

Solve each problem. The amount, in billions of dollars, that Americans spent on their pets from 2003 to 2016 can be approximated by substituting a given year for \(x\) in the following expression. $$2.493 x-4962$$ (Data from American Pet Products Manufacturers Association.) Find the amount spent in each year. Round answers to the nearest tenth. (a) 2003 (b) 2010 (c) 2016 (d) How did the amount Americans spent on their pets change from 2003 to \(2016 ?\)

Residents of Linn County, Iowa, in the Cedar Rapids Community School District can use the expression $$(v \times 0.5485-4850) \div 1000 \times 31.44$$ to determine their property taxes, where \(v\) is assessed home value. (Source: The Gazette.)Use this expression to calculate, to the nearest dollar, the amount of property taxes that the owner of a home with each of the following values would pay. Follow the rules for order of operations. $$ \$ 200,000 $$

The distributive property can be used to mentally perform calculations. $$\begin{array}{l}38 \cdot 17+38 \cdot 3 \\\=38(17+3) \\\=38(20) \\\=760\end{array} $$Use the distributive property to calculate each value mentally. $$ 27 \cdot 60+27 \cdot 40 $$
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