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Chapter 0: Problem 137

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

Short Answer

Expert verified
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 by step solution

01

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.
02

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.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$4^{-2}<4^{-3}$$

Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$\frac{x^{2}+6 x+5}{x^{2}-25}$$

Determine whether each statement in Exercises 43鈥�50 is true or false. $$-\pi \geq-\pi$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

Evaluate each algebraic expression for the given value or values of the variable(s). $$6+5(x-6)^{3}, \text { for } x=8$$
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