Problem 137 - College Algebra

Question

If \(n\) is a natural number, what does \(b^{n}\) mean? Give an example with your explanation.

Step-by-Step Solution

Answer

\(b^{n}\) means that the base \(b\) is multiplied by itself \(n\) times. For e.g. if \(b = 2\) and \(n = 3\), then \(b^{n} = 2^{3} = 2 \times 2 \times 2 = 8\).

Step 1: Understand the terms

An exponent refers to the number of times a number is multiplied by itself. In the expression \(b^{n}\), \(b\) is the base and \(n\) is the exponent. The natural numbers are the set of positive integers, usually starting from either 1 or 0.

Step 2: Interpretation of \(b^{n}\)

The expression \(b^{n}\) means that the base \(b\) is multiplied by itself \(n\) times. This is known as exponentiation.

Step 3: Provide an Example

For instance, if \(b = 2\) and \(n = 3\), then \(b^{n}\) is \(2^{3}\), which means 2 is multiplied by itself 3 times, i.e., \(2 \times 2 \times 2 = 8\). So, \(2^{3} = 8\).