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Chapter 1: Problem 104

In the following exercises, simplify each expression. $$ 8^{3} $$

Short Answer

Expert verified
The simplified expression is 512.

Step by step solution

01

Identify the base and the exponent

In the given expression, identify the base and the exponent. The base is 8 and the exponent is 3.
02

Understand the meaning of the exponent

The exponent indicates how many times the base is multiplied by itself. Here, 8 is multiplied by itself 3 times.
03

Multiply the base by itself the number of times indicated by the exponent

Calculate the expression by multiplying the base 8 three times: the base 8 three times: 8 脳 8 脳 8 = 512.

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Key Concepts

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

identifying bases and exponents
When you first see an expression with an exponent, the initial task is to identify the base and the exponent.
The base is the number that is going to be multiplied.
The exponent, sometimes called the power, tells you how many times to multiply the base by itself.
For example, in the expression \(8^{3}\), the base is 8 and the exponent is 3. This means you will multiply 8 by itself three times.
understanding exponents
Exponents can seem confusing at first, but they are simply a shorthand way of showing repeated multiplication.
Instead of writing \(8 \times 8 \times 8\), you use the exponent to simplify this to \(8^{3}\).
The exponent tells you how many copies of the base to multiply together. Here, the exponent 3 means you have three 8s multiplied together. Understanding this concept will help make simplifying exponents much easier.
multiplying bases
Once you have identified the base and the exponent and understand what the exponent means, you can multiply the base by itself.
Using our example \(8^{3}\), you multiply the base 8 three times: 8 脳 8 = 64, and then 64 脳 8 = 512.
This gives you the final simplified result: \(8^{3} = 512\).
If you follow these steps each time, simplifying expressions with exponents becomes a straightforward process.

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