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Chapter 1: Problem 10

Write an exponential expression with 3 as the base and 8 as the exponent.

Short Answer

Expert verified
3^8

Step by step solution

01

Identify the Base

The base in the given problem is 3.
02

Identify the Exponent

The exponent in the given problem is 8.
03

Write the Exponential Expression

Combine the base and the exponent to form the exponential expression: 3^8.

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Key Concepts

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

Understanding the Base
In exponential expressions, the base is the number being multiplied by itself. For the expression 3^8, the base is 3.

The base is the main number that we multiply over and over. It forms the foundation of the exponential expression.

For example, if you see 5^4, the base is 5. We will multiply 5 by itself four times. Remember, the base stays the same during multiplication.
Exploring the Exponent
The exponent is the small number written to the upper right of the base. It tells you how many times to multiply the base by itself.

In 3^8, 8 is the exponent. This means you multiply 3 by itself eight times.

Exponents are key in determining how many repeats of multiplication you need. For example, in 2^3, you'll multiply 2 * 2 * 2. The exponent helps you understand the length of the multiplication.
Importance of Mathematical Notation
Mathematical notation is a system of symbols used to represent numbers and operations.

In exponential expressions, we use a compact form of notation to avoid writing out long multiplications.

For example, instead of writing 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3, we write 3^8.

This notation is both time-saving and makes our calculations neat and clear. Mathematical notation helps in communicating complex concepts in a simple way.
Grasping the Concept of Powers
Powers are a way to express repeated multiplication of the same number. The number being multiplied is the base, and the power is indicated by the exponent.

In 3^8, we say 3 is raised to the 8th power.

Powers are very useful in mathematics and occur frequently in problems involving areas, volumes, and growth calculations.

Understanding powers simplifies many math problems where repeated multiplication is needed.
Introduction to Exponential Functions
Exponential functions involve an exponent and are used to model many real-world situations. These functions can grow rapidly, which is why they are important in fields like finance, biology, and physics.

An exponential function has the general form: f(x) = a * b^x, where:
  • a is a constant,
  • b is the base,
  • x is the exponent or variable.
For example, in finance, compound interest is calculated using an exponential function. Understanding these functions enhances our ability to model and solve practical problems.

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Most popular questions from this chapter

Fill in the blank with the inequality symbol \(<\) or \(>\). $$5 \square 7$$

Perform the indicated operation by using a calculator. $$\begin{array}{r} 82,025,160 \\ -79,118,705 \\ \hline \end{array}$$

Perform the indicated operation by using a calculator. $$\begin{array}{r} 45,418 \\ 81,990 \\ 9,063 \\ +56,309 \\ \hline \end{array}$$

For each English sentence, write a mathematical expression and simplify. Divide 9 into 108.

Show how checking by multiplication can help us remember that \(0 \div 5=0\) and that \(5 \div 0\) is undefined.
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