Problem 33 - Elementary Algebra

Question

\(2^{3}\)

Step-by-Step Solution

Answer

8

Step 1 - Understand the problem

Recognize that you need to calculate the value of the expression involving an exponentiation: \[2^3\]

Step 2 - Identify the base and the exponent

In the expression \(2^3\), the number 2 is the base, and the number 3 is the exponent. This means you will multiply the base by itself as many times as indicated by the exponent.

Step 3 - Perform the multiplication

Multiply the base by itself the number of times indicated by the exponent: \[2 \times 2 \times 2\]

Step 4 - Calculate the result

First, multiply 2 by 2 to get 4. Then multiply 4 by 2 to get 8. So, \[2^3 = 8\]

Key Concepts

base and exponent

When you see an expression like \(2^3\), you're dealing with exponentiation.
This involves two crucial parts: the base and the exponent. The base is the number that will be multiplied by itself. In this case, it's 2.
The exponent tells you how many times to multiply the base by itself. Here, the exponent is 3. So, in \(2^3\), you are essentially calculating \2 \times 2 \times 2\.

multiplication

Multiplication is the process of combining groups of equal size.
In the context of exponentiation, you use multiplication to repeatedly multiply the base. For \(2^3\), you multiply 2 by 2, and then multiply the result by 2 again.
Let's break it down:

• First, multiply 2 (base) by 2 to get 4.
• Next, take that result (4) and multiply by 2 again to get 8.

This shows that \(2^3 = 2 \times 2 \times 2 = 8\).

powers of numbers

The expression \(2^3\) is an example of powers of numbers.
In mathematics, powers are a way to express repeated multiplication of the same number. The notation \(a^n\) tells you to multiply the base \(a\) by itself \(n\) times.
For example, \(3^2\) means \(3 \times 3 = 9\), and \(4^3\) means \4 \times 4 \times 4 = 64\.
Understanding powers of numbers helps in simplifying and solving many mathematical problems. It’s a fundamental concept that recurs in various areas of math.