/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 75 Simplify. Do not use negative ex... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 75

Simplify. Do not use negative exponents in the answer. $$ -3^{-2} $$

Short Answer

Expert verified
-1/9

Step by step solution

01

Understand the Negative Exponent

A negative exponent indicates that the base should be reciprocated. For example, if you have a term like \( a^{-n} \), it can be written as \( \frac{1}{a^n} \).
02

Apply the Rule to the Given Problem

Apply the negative exponent rule to \( -3^{-2} \). This means you will take the reciprocal and change the exponent to positive. So, \( -3^{-2} \) becomes \( -\frac{1}{3^2} \).
03

Simplify the Positive Exponent

Now, calculate \( 3^2 \). This is equal to 3 * 3, which is 9. Therefore, \( -\frac{1}{3^2} \) simplifies to \( -\frac{1}{9} \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

negative exponents
Understanding negative exponents is crucial for simplifying mathematical expressions. When you see a negative exponent, it tells you to take the reciprocal of the base and then apply the positive exponent to it. For example, if you have a term like \(a^{-n}\), it can be transformed into \(\frac{1}{a^n}\). This means that instead of multiplying \(a\) \(n\) times, you are dividing 1 by \(a\) \(n\) times. This concept may initially seem tricky, but it helps to always remember to flip the base to the denominator and make the exponent positive.
reciprocal
The term 'reciprocal' means flipping a fraction upside down. For a number \(a\), its reciprocal is \(\frac{1}{a}\). This is an essential concept when dealing with negative exponents. When you have, for example, \(3^{-2}\), you need to transform it using its reciprocal. This becomes \(\frac{1}{3^2}\). This flipping is necessary to change the exponent from negative to positive. Using reciprocals helps to simplify expressions more easily and avoid confusion with negative powers.
simplification of exponents
Simplifying exponents involves reducing expressions to their simplest form. The steps to do this include:
  • Identify if the exponent is negative.
  • If negative, take the reciprocal to make the exponent positive.
  • Calculate the power of the base with the now positive exponent.
For example, to simplify \(-3^{-2}\):
  • First, note the negative exponent in \(-3^{-2}\).
  • Change to its reciprocal: \(-\frac{1}{3^2}\).
  • Then, calculate \(3^2\), which is 9.
  • Finally, the simplification results in \(-\frac{1}{9}\).
Breaking down these steps makes the process straightforward.
positive exponents
Once you have dealt with the negative exponent by applying the reciprocal, the next step is to calculate using the positive exponent. Positive exponents are more straightforward. They simply mean you multiply the base by itself as many times as indicated by the exponent. For instance, for \(3^2\), you multiply 3 by itself: 3 * 3, which equals 9. Understanding this is fundamental when progressing from dealing with negative exponents to simplifying fully. In our example, transforming \(-3^{-2}\) to \(-\frac{1}{3^2}\) leads us to finally compute \(-\frac{1}{9}\) after simplification with positive exponents.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Factor completely. $$ z^{12}-1 \quad[5.6] $$

Find an equation of variation in which: \(y\) varies jointly as \(x\) and \(z,\) and \(y=105\) when \(x=14\) and \(z=5\).

Simplify. Do not use negative exponents in the answer. $$ \frac{24 a^{-4} c^{-8}}{16 a^{5} c^{-7}} $$

Explain the difference between adding rational expressions and solving rational equations.

The intensity I of light varies inversely as the square of the distance \(d\) from the light source. The following table shows the illumination from a light source at several distances from the source. What is the illumination 2.5 ft from the source?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.