/*! 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 16 Evaluate. $$ 2^{6} $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 16

Evaluate. $$ 2^{6} $$

Short Answer

Expert verified
64

Step by step solution

01

Understand the Expression

The expression to evaluate is an exponent, specifically, the base 2 raised to the power of 6. This is represented as \(2^{6}\).
02

Expand the Exponentiation

To understand what \(2^{6}\) means, expand it as follows: \(2^{6} = 2 \times 2 \times 2 \times 2 \times 2 \times 2\).
03

Perform the Multiplication

Now, multiply the numbers step-by-step:1. \(2 \times 2 = 4\)2. \(4 \times 2 = 8\)3. \(8 \times 2 = 16\)4. \(16 \times 2 = 32\)5. \(32 \times 2 = 64\)Thus, \(2^{6} = 64\).

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.

powers of numbers
The concept of powers of numbers, also known as exponentiation, is a fundamental operation in mathematics. It involves raising a base number to an exponent. In simpler words, it means multiplying the base by itself multiple times. For instance, in the exercise, we are asked to calculate \( 2^6 \). Here, 2 is the base and 6 is the exponent. This tells us that we need to multiply 2 by itself 6 times: \( 2 \times 2 \times 2 \times 2 \times 2 \times 2 \). Understanding how to expand and evaluate powers is crucial for mastering various areas of math.
multiplication
Multiplication is one of the basic arithmetic operations and a key step in evaluating powers of numbers. It is the process of adding a number to itself a certain number of times. For example, to evaluate \( 2^6 \), we expanded it to \( 2 \times 2 \times 2 \times 2 \times 2 \times 2 \). Let's break down the multiplication:
  • First, multiply 2 by 2 to get 4.
  • Next, multiply 4 by 2 to get 8.
  • Then, multiply 8 by 2 to get 16.
  • After that, multiply 16 by 2 to get 32.
  • Finally, multiply 32 by 2 to get the answer, 64.
This step-by-step multiplication helps us understand the exponentiation process better.
basic arithmetic operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations form the foundation of most mathematical concepts. Understanding how to perform these operations correctly is essential for solving various math problems. In our example, evaluating \( 2^6 \), we relied on repeated multiplication.
Mastering these basic operations is not only vital for tackling more complex mathematical problems but also for everyday calculations. Practicing problems involving these operations enhances computational skills and boosts confidence in handling numbers.

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

Round to the nearest ten. $$ 48 $$

Write exponential notation. $$ 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 $$

Solve. Be sure to check. $$ 162=9 \cdot m $$

Write each number in standard notation. Fifty thousand, three hundred twenty-four

A local television station plans to air the 177 episodes of the long-running comedy series Seinfeld. If the station airs 5 episodes per week, how many full weeks will pass before it must begin re-airing previously shown episodes? How many unaired episodes will be shown the following week before the previously aired episodes are rerun?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Mechanics 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.