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Chapter 4: Problem 7

In Exercises 1-8, evaluate the expression. \(10^{5}\)

Short Answer

Expert verified
The evaluation of the expression \(10^{5}\) is 100000.

Step by step solution

01

Understanding Exponentiation

In the given expression \(10^{5}\), the base is 10 and the exponent is 5. This means that we need to multiply the base, 10, by itself 5 times.
02

Performing the Calculation

We multiply 10 by itself 5 times: \(10 \times 10 \times 10 \times 10 \times 10\). This gives us the result 100000.

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Key Concepts

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

Base and Exponent
In the world of mathematics, exponentiation is a crucial concept. It helps simplify complex calculations. An expression like \(10^5\) involves two main components, the base and the exponent.
- **Base**: It refers to the number being multiplied. In our example, the base is 10.- **Exponent**: This indicates how many times the base multiplies by itself. Here, 5 is the exponent.
Exponentiation significantly reduces the effort needed to write large calculations. Instead of writing \(10\times10\times10\times10\times10\), we simply write \(10^5\).
The notation is especially useful in fields such as science and finance where handling large numbers is common.
Multiplication
Multiplication is the process of adding a number to itself a certain number of times. It's one of the basic arithmetic operations, represented by the symbol \(\times\).
When dealing with exponentiation, multiplication plays an integral role. The exponent tells you how many times you need to multiply the base by itself. For example, in \(10^5\), you perform the multiplication:
  • First multiplication: \(10 \times 10 = 100\)
  • Second multiplication: \(100 \times 10 = 1000\)
  • Third multiplication: \(1000 \times 10 = 10000\)
  • Fourth multiplication: \(10000 \times 10 = 100000\)
Practicing these repeated multiplication steps strengthens your understanding of multiplication and how we arrive at significant figures in exponentiation calculations.
Mathematical Expressions
Mathematical expressions are combinations of numbers, operators, and symbols that represent a value or relationship. For example, \(10^5\) is a simple mathematical expression.
These expressions allow for a compact representation of complex calculations and ideas. They often include:
  • Numbers and constants (like 10 in our example).
  • Operators, such as addition, subtraction, multiplication, division, and exponentiation (like the exponent \(^5\)).
  • Grouping symbols such as parentheses \(()\) to indicate the order of operations.
Understanding how to construct and deconstruct mathematical expressions is essential for problem-solving in math and real-world applications.

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Most popular questions from this chapter

In Exercises 19-32, mentally convert each base ten numeral to a numeral in the given base. 5 to base two

In Exercises 13鈥�24, subtract in the indicated base. $$ \begin{array}{r} 712_{\text {nine }} \\ -483_{\text {nine }} \\ \hline \end{array} $$

Make Sense? In Exercises 76-79, determine whether each statement makes sense or does not make sense, and explain your reasoning. Because (0) represents 100 and \(\cap\) represents 10 in the Egyptian numeration system, (5) \(\cap\) represents \(100+10\), or 110 , and (6) represents \(100-10\), or 90 .

In Exercises 19-32, mentally convert each base ten numeral to a numeral in the given base. 6 to base two

In Exercises 19-32, mentally convert each base ten mumeral to a numeral in the given base. 11 to base seven
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