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Chapter 5: Problem 146

Explain the negative exponent rule and give an example.

Short Answer

Expert verified
The negative exponent rule states that \(a^{-n} = 1/a^{n}\) for any non-zero number a. For example, \(2^{-3}\) can be written as \(1/2^{3}\), which simplifies to \(1/8\).

Step by step solution

01

Understand the Negative Exponent Rule

In mathematics, the negative exponent rule states that any base with a negative exponent is equal to its reciprocal with the exponent made positive. In other words, \(a^{-n} = 1/a^{n}\) for any number a 鈮� 0. This can also be understood as replacing the negative exponent with a positive one by placing the base and its exponent in the denominator of a fraction whose numerator is one.
02

Apply the Negative Exponent Rule

Let's say we have an example where a = 2 and n = 3, i.e., we must find the value for \(2^{-3}\). According to the negative exponent rule, we change the -3 exponent to a positive 3 and place the base 2 in the denominator of a fraction. So, the result is \(2^{-3} = 1/2^{3}\).
03

Simplify the Expression

Now that we've applied the rule, we need to simplify the expression \(1/2^{3}\). The exponent tells us to multiply the base by itself for the number of times shown by the exponent. So, \(2^{3} = 2 * 2 * 2 = 8\), and our fraction becomes \(1/8\).

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