/*! 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 27 Evaluate each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 27

Evaluate each expression. $$ (-3)^{-4} $$

Short Answer

Expert verified
\((-3)^{-4} = \frac{1}{81}\)

Step by step solution

01

- Identify the expression

The expression given is \((-3)^{-4}\). The goal is to evaluate this expression.
02

- Apply the negative exponent rule

Using the rule that \(a^{-n} = \frac{1}{a^n}\), rewrite the expression: \((-3)^{-4} = \frac{1}{(-3)^4}\).
03

- Evaluate the positive exponent

Calculate \((-3)^4\). Since any number raised to an even power results in a positive number, calculate \((-3)^4 = 81\).
04

- Simplify the expression

Combine the results from the previous steps: \((-3)^{-4} = \frac{1}{81}\).

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 exponent rule
The negative exponent rule is an essential concept in algebra. It states that any nonzero number raised to a negative exponent is equal to the reciprocal of that number raised to the opposite positive exponent.

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

Write each product as a sum of terms. Write answers with positive exponents only. Simplify each term. $$ \frac{1}{2 p}\left(4 p^{2}+2 p+8\right) $$

Find each product. $$ -5 r(r+1)^{3} $$

The special product $$ (x+y)(x-y)=x^{2}-y^{2} $$ can be used to perform some multiplication problems. Here are two examples. $$ \begin{aligned} 51 \times 49 &=(50+1)(50-1) \\ &=50^{2}-1^{2} \\ &=2500-1 \\ &=2499 \end{aligned} \quad | \begin{aligned} 102 \times 98 &=(100+2)(100-2) \\ &=100^{2}-2^{2} \\ &=10,000-4 \\ &=9996 \end{aligned} $$ Once these patterns are recognized, multiplications of this type can be done mentally. Use this method to calculate each product mentally. $$ 201 \times 199 $$

Each statement contains a number in boldface italics. Write the number in scientific notation. In \(2007,\) the leading U.S. advertiser was the Procter and Gamble Company, which spent approximately 5,230,000,000 dollars. (Source: Crain Communications, Inc.)

Divide each polynomial by \(3 x^{2}\). See Examples \(1-3\) $$ 4 x^{4}+3 x^{3}+2 x $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Statistics

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.