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Chapter 1: Problem 7

Write \(1 / x\) as \(x\) to some power.

Short Answer

Expert verified
\(1 / x\) can be written as \(x^{-1}\).

Step by step solution

01

Understanding negative exponents

The first step is to understand that a number raised to a negative exponent results in the reciprocal of the number raised to the positive exponent. In other words, if you have \(a^{-n}\), this is equal to \(1 / a^n\).
02

Applying knowledge of negative exponents

Next, apply what was just explained to the question at hand. If \(1 / x\) needs to be represented as \(x\) to the power of something, the something is -1. Since from step 1, we know that \(a^{-n} = 1/a^n \) and applying this to the fraction gives us \(x^{-1}\).

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