Problem 137 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The expression \(b^{n}\) signifies the process of multiplying the base \(b\) by itself \(n\) times. For example, \(5^{2}\) denotes 5 multiplied by itself twice, equalling 25.

Step 1: Explanation of exponentiation

\(b^{n}\) is an expression that represents exponentiation. Here, \(b\) is the base, and \(n\) is the exponent or power. This means that the base \(b\) is multiplied by itself \(n\) times. For instance, if \(b = 2\) and \(n = 3\), then \(2^{3} = 2 \cdot 2 \cdot 2 = 8\). This is because the base 2 is multiplied by itself 3 times.

Step 2: Example of exponentiation

Let's look at an example. If we take \(b = 5\) and \(n = 2\), then \(5^{2} = 5 \cdot 5 = 25\). Thus, \(5^{2}\) means 5 multiplied by itself 2 times.