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Chapter 5: Problem 3

For Exercises \(3-10\), expand the powers of 10 or \(\frac{1}{10}\). $$10^{2}$$

Short Answer

Expert verified
10^2 = 100.

Step by step solution

01

Identify the Power

The given expression is \(10^{2}\). This indicates that 10 is raised to the power of 2.
02

Interpret the Exponent

The exponent '2' means that the base, which is 10, should be multiplied by itself two times.
03

Perform the Multiplication

Multiply the base (10) by itself: \(10 \times 10 = 100\).

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Key Concepts

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

Exponents
When dealing with exponents, you are essentially using a form of shorthand for repeated multiplication. The expression \(10^2\) involves raising the base number 10 to the power of 2. This means multiplying 10 by itself, two times. The exponent tells you the number of times the base is multiplied. For instance, in \(10^3\), you would multiply 10 by itself three times. Exponents are tremendously useful in simplifying large numbers and expressions. Instead of writing out all the multiplications, you can use an exponent to show repeated multiplication. This saves time and avoids clutter.
Multiplication
Multiplication is a basic arithmetic operation that involves finding the product of numbers. In the context of exponents, multiplication is crucial because an exponent indicates how many times you multiply the base by itself. Let's break down \(10^2\) again: Here, 10 is your base and 2 is the exponent. The calculation is straightforward: you multiply 10 by itself. So, \(10 \times 10 = 100\). Understanding how to perform these multiplications quickly and accurately is key when working with exponents. Practicing multiplication can also help you become faster and more confident in dealing with larger numbers.
Basic Arithmetic
Basic arithmetic encompasses the fundamental operations like addition, subtraction, multiplication, and division. These operations form the building blocks for more complex mathematical concepts. Specifically, in expanding powers of 10, the multiplication aspect of basic arithmetic is in use. For example, in calculating \(10^2\), you apply the principle of multiplying 10 by itself鈥攁 straightforward task within basic arithmetic. Mastering these elementary operations will make understanding advanced topics, including exponents, much easier. Basic arithmetic skills are essential not just in math classes but in everyday problem-solving situations as well.

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