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Chapter 10: Problem 593

Simplify. $$(8 n)^{-1}$$

Short Answer

Expert verified
\(\frac{1}{8n}\).

Step by step solution

01

Understanding the Negative Exponent

A negative exponent means that the base (in this case, the term \(8n\)) should be flipped to its reciprocal. Essentially, \((a^b)^{-1} = \frac{1}{a^b}\).
02

Apply the Rule

Using the rule from Step 1, rewrite the expression \((8n)^{-1}\) as \(\frac{1}{8n}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reciprocal
Let's start by understanding what a reciprocal is. A reciprocal of a number is simply one over that number. For example, the reciprocal of 5 is \(\frac{1}{5}\). This concept can also be applied to variables and more complex terms. When working with expressions that involve negative exponents, such as \((8n)^{-1}\), we use the rule that states we take the reciprocal of the base term. In this case, the base is \(8n\). By flipping it to \(\frac{1}{8n}\), we've applied the reciprocal rule properly.
Simplifying Expressions
Simplifying expressions is a crucial skill in math, especially in prealgebra and algebra. Let's break this down with our example. Starting with \((8n)^{-1}\), we need to make this expression simpler. Recognize that a negative exponent indicates taking the reciprocal of the base term. Therefore, \((8n)^{-1} \) becomes \(\frac{1}{8n}\). Once simplified, we ideally want our expressions to be in their simplest form for easier interpretation and further calculations. Always follow rules like the exponent rules and the order of operations for accurate results.
Prealgebra Concepts
In prealgebra, we often encounter exponents, both positive and negative. Understanding how to handle these exponents is fundamental. A negative exponent, for instance, does not make the value negative. Instead, it signifies the reciprocal. As with the term \((8n)^{-1}\), turning the negative exponent into a positive one involves rewriting it as \(\frac{1}{8n}\). It's also essential to grasp other prealgebra concepts like basic arithmetical operations and the properties of numbers. Mastering these principles provides a strong foundation for tackling more advanced topics in algebra and beyond.

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Most popular questions from this chapter

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Simplify each expression. $$n \cdot n^{4}$$
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