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Chapter 0: Problem 18

Write each expression using exponents. $$ (0.1)(0.1)(0.1)(0.1)(0.1)(0.1) $$

Short Answer

Expert verified
The expression can be written as \(0.1^6\).

Step by step solution

01

Identify the base number

The base number is the number that is repeatedly multiplied. In this expression, the number 0.1 is multiplied several times.
02

Count the number of times the base is repeated

Count how many times the base number 0.1 appears in the expression. There are 6 instances of 0.1.
03

Write the expression using exponents

Since the base number 0.1 is used 6 times, it can be written in exponential form as \(0.1^6\). This simplifies the expression by showing the repeated multiplication in a compact form.

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Key Concepts

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

base number
Understanding the base number is crucial in algebra, especially when dealing with exponents. The base number is the one that you multiply by itself, repeatedly. For instance, in the expression \((0.1)(0.1)(0.1)(0.1)(0.1)(0.1)\), the base number is \(0.1\). This is because it's the number being repeated in the multiplication process. Without identifying the base, you won't be able to simplify the expression. Always look for the number that stays constant and appears multiple times in the multiplication.
repeated multiplication
Repeated multiplication is a key concept when working with exponents. It's the process of taking one number (the base) and multiplying it by itself several times. In our example, \(0.1 \times 0.1 \times 0.1 \times 0.1 \times 0.1 \times 0.1\), \(0.1\) is multiplied by itself 6 times. Instead of writing out all the multiplications, using exponents helps to simplify this expression. Recognizing this pattern allows students to write and understand more complex mathematical concepts with ease.
exponential form
Exponential form is a shorthand way to write expressions involving repeated multiplication. It uses a base number and an exponent. The base number is the one being multiplied, and the exponent tells you how many times to multiply the base by itself. In the problem, \(0.1\) is the base, and it鈥檚 multiplied by itself 6 times. Therefore, the exponential form of the expression is \(0.1^6\). This notation is much more compact and easier to work with than writing out each multiplication.

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Most popular questions from this chapter

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