/*! 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 69 Evaluate each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 69

Evaluate each expression. $$ 3^{4} $$

Short Answer

Expert verified
The value of \(3^4\) is 81.

Step by step solution

01

Understand the Base and Exponent

The expression \(3^4\) is composed of a base 3 and an exponent 4. The exponent indicates that the base is multiplied by itself a specific number of times.
02

Expand the Exponentiation

To solve \(3^4\), we need to multiply the base 3 by itself 4 times. This means \(3^4 = 3 \times 3 \times 3 \times 3\).
03

Perform Sequential Multiplication

Start multiplying sequentially: first calculate \(3 \times 3 = 9\), then multiply the result by the next 3: \(9 \times 3 = 27\). Finally, multiply this result by the last 3: \(27 \times 3 = 81\).
04

Confirm the Result

Verify that all steps have been followed correctly and confirm that the final result matches the expected calculation: \(3 \times 3 = 9\), \(9 \times 3 = 27\), and \(27 \times 3 = 81\).

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.

Understanding Base and Exponent
In exponentiation, the expression is composed of two primary parts: the base and the exponent. The base is the number that is subject to repeated multiplication. The exponent indicates how many times the base is multiplied by itself. For instance, in the expression \(3^4\), the number 3 is the base, and the number 4 is the exponent. This means that we are to multiply 3 by itself 4 times. Exponents simplify expressions of repeated multiplication by summarizing them in a compact form.
The Role of Multiplication in Exponentiation
Multiplication is a mathematical operation where a number, known as the multiplicand, is added to itself a number of times as defined by another number, the multiplier. In exponentiation, multiplication is at the core because the base is multiplied by itself as many times as the number of the exponent. Taking our example \(3^4\), multiplication occurs as follows: \(3 \times 3\), then that product is multiplied by another 3, and so forth. Hence, multiplication turns a lengthy addition process into a more efficient evaluation.
Performing Sequential Multiplication
Sequential multiplication involves performing multiplication step-by-step, one pair of numbers at a time. In the example of \(3^4\), we start by multiplying the first two 3's: \(3 \times 3 = 9\). Then, take this result (9) and multiply by the next 3: \(9 \times 3 = 27\). Finally, multiply 27 by the last 3 to yield the final answer: \(27 \times 3 = 81\). By breaking it into sequential steps, we simplify the process and reduce errors, ensuring accurate results.

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

Two angles are supplementary if their sum is \(180^{\circ} .\) The larger angle below measures eight degrees more than three times the measure of the smaller angle. If \(x\) represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.

The graph shows the number of U.S. Starbucks locations from 2002 to \(2008 .\) The height of the graph for each year shown corresponds to the number of Starbucks locations in the United States. Use this graph to answer . (We study graphs such as this further in Section 6.1.) Between which two years did the greatest increase in the number of Starbucks locations occur?

Ben Holladay bowled 146 and 201 in his first two games. What must he bowl in his third game to have an average of at least \(180 ?\) (Hint: The average of a list of numbers is their sum divided by the number of numbers in the list.)

In your own words, explain why a solution of a word problem should be checked using the original wording of the problem and not the equation written from the wording.

Evaluate each expression for the given values. See Section \(1.8 .\) \(2 W+2 L ; \quad W=7\) and \(L=10\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.