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Chapter 5: Problem 31

Write each number without exponents. $$ 6.21 \times 10^{0} $$

Short Answer

Expert verified
6.21

Step by step solution

01

Understand the Exponent

In this exercise, the exponent is 0. When any number is raised to the power of 0, the value is always 1. Therefore, the expression is really 6.21 multiplied by 1.
02

Simplify the Expression

Since 6.21 is being multiplied by 1, the result is simply 6.21. Thus, there are no additional calculations needed.

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Key Concepts

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

Exponents
Exponents are a way to represent repeated multiplication of the same number. For example, instead of writing 10 multiplied by itself three times (10 * 10 * 10), we use an exponent and write it as 10^3. This is much simpler and cleaner.

When dealing with exponents, certain rules apply. One of the most important rules to remember is that any number raised to the power of 0 is always equal to 1. For example, 10^0 equals 1. This principle was used in the exercise where 6.21 is multiplied by 10^0. Since 10^0 is equal to 1, the multiplication simplifies quickly.

Working with exponents helps in making calculations more manageable and expressing large or small numbers efficiently.
Simplifying Expressions
Simplifying expressions means reducing them to their simplest form. This usually involves performing the necessary operations to combine or reduce terms. In the given exercise, the expression 6.21 * 10^0 needed to be simplified.

First, we recognized that 10^0 equals 1. By substituting 1 for 10^0, the expression became 6.21 * 1. Simplifying further, multiplying any number by 1 does not change its value. Thus, the expression simplifies to just 6.21.

Mastering the skill of simplifying expressions will make solving complex algebra problems easier, ensuring that calculations are as straightforward as possible.
Multiplication
Multiplication is a fundamental arithmetic operation that involves adding a number to itself a certain number of times. It is signified by the symbol '*'.

In the exercise, the multiplication operation involved 6.21 and 1 (since 10^0 equals 1). Multiplying any number by 1 results in the original number itself. Therefore, multiplying 6.21 by 1 does not change its value, and the answer remains 6.21.

Understanding basic multiplication is crucial as it is used widely in algebra and higher mathematics. It forms the basis for many mathematical concepts, including exponents and simplifying expressions.

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