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Chapter 10: Problem 342

In the following exercises, simplify. (a) 6\(m^{-1} \quad\) (b) \((6 m)^{-1}\) (c) \((-6 m)^{-1}\)

Short Answer

Expert verified
(a) \(\frac{6}{m}\) (b) \(\frac{1}{6m}\) (c) \(\frac{1}{-6m}\)

Step by step solution

01

Simplify 6m^{-1}

To simplify the expression 6m^{-1}, remember that a negative exponent indicates a reciprocal. Thus, 6m^{-1} can be rewritten as \ \(\frac{6}{m}\).
02

Simplify (6m)^{-1}

For the expression (6m)^{-1}, apply the property of negative exponents again. This can be rewritten as the reciprocal of the entire term: \ \((6m)^{-1} = \frac{1}{6m}\).
03

Simplify (-6m)^{-1}

Similar to the previous step, simplify the expression (-6m)^{-1} by taking the reciprocal: \ \((-6m)^{-1} = \frac{1}{-6m}\).

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Key Concepts

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

Reciprocal
The reciprocal of a number is essentially one divided by that number. In mathematical terms, the reciprocal of a number 'a' is written as \(\frac{1}{a}\). This concept is crucial when dealing with negative exponents.

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