/*! 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 86 Evaluate: $$ 2^{6} $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 86

Evaluate: $$ 2^{6} $$

Short Answer

Expert verified
The value of \(2^6\) is 64.

Step by step solution

01

Identify the Base and Exponent

The given expression is in the form of an exponent. The base is 2 and the exponent is 6. This means you need to multiply the base (2) by itself as many times as indicated by the exponent (6).
02

Write The Multiplication Form

From the previous step, we know we have to multiply 2 by itself 6 times: \( 2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \).
03

Perform the Multiplications

First, multiply the first pair: \( 2 \times 2 = 4 \). Then, continue multiplying the result by 2 over and over: \( 4 \times 2 = 8 \), \( 8 \times 2 = 16 \), \( 16 \times 2 = 32 \), \( 32 \times 2 = 64 \).
04

Write the Final Answer

The result of multiplying 2 by itself 6 times is 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.

Base and Exponent Identification
In the expression \( 2^{6} \), we need to identify the base and the exponent. This step is crucial because it helps us understand what needs to be done to solve the exponent.

The base is the number that is being multiplied. Here, our base is 2. The exponent, which is 6 in this case, tells us how many times to multiply the base by itself.

To summarize:
  • Base: The number being multiplied repeatedly, which is 2.
  • Exponent: The number of times the base is multiplied by itself, which is 6.
Recognizing the base and exponent allows us to write the expression in its multiplication form.
Multiplication Form of Exponents
After identifying the base and exponent, the next step is to convert the exponent expression into multiplication form.

This means we'll write the base being multiplied by itself as many times as the value of the exponent. For \( 2^{6} \), we'll multiply the base (2) by itself 6 times:
\[ 2^{6} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \]

Breaking the exponent into a string of multiplications helps us to see exactly what needs to be calculated. Each '2' represents one term in the multiplication sequence, and we have six '2's written out.

Using the multiplication format makes it clear and straightforward, especially useful for visualizing and verifying each step.
Step-by-Step Multiplication
Now that we have our multiplication form, we can start to multiply step-by-step.

First, multiply the first two numbers: \[ 2 \times 2 = 4 \]
Now, multiply the result by the next 2:
\[ 4 \times 2 = 8 \]
Continue this process:
\[ 8 \times 2 = 16 \]
\[ 16 \times 2 = 32 \]
\[ 32 \times 2 = 64 \]

At each step, we're simply multiplying the previous result by 2. This approach ensures accuracy by breaking down the problem into smaller, manageable parts.

Finally, we reach our answer:
\[ 2^{6} = 64 \]
Simplifying the calculations step-by-step removes confusion and makes it easy to track your progress.

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

Add. $$ 17+3.24+0.256+0.3689 $$

Simplify. $$ 200+40 \div 4 $$

A group of 4 students pays \(\$ 47.84\) for lunch and splits the cost equally. What is each person's share?

Estimate. Indicate which of the choices is an appropriate estimate. \(0.0713 \div 1.94\) a) 3.5 b) 0.35 c) 0.035 d) 35

A person weighing \(150 \mathrm{lb}\) burns 7.3 calories per minute while mowing a lawn with a power lawnmower. How many calories would be burned in \(2 \mathrm{hr}\) of mowing?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.