Problem 1 \(2 \cdot 2 \cdot 2 \cdot 2 \cdo... [FREE SOLUTION]

91影视

Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 1

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$

Short Answer

Expert verified

The answer is 64.

Step by step solution

Understanding the Problem

We have the number 2 being multiplied by itself six times, which can be expressed as $2^6$.

Applying the Rule of Exponentiation

Using the rule of exponentiation, $2^6 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$, it is easy to determine that our problem simplifies to $2^6$.

Solving the Problem

We calculate $2^6$, which equals 64.

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Key Concepts

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

Powers of Numbers

When we talk about the powers of numbers, we are referring to a type of multiplication known as exponentiation. This is when a number, called the base, is multiplied by itself many times. The exponent tells us how many times the base is used as a factor. For example, in the expression $2^6$, 2 is the base, and 6 is the exponent. This means we multiply 2 by itself six times.

The base is the number that we repeatedly multiply.
The exponent shows the number of times to use the base in multiplication.

This concept helps us work with very large or very repeated multiplications much more easily.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form. This means breaking down longer, more complicated expressions into shorter ones that are easier to understand. When dealing with powers of numbers, this often means recognizing repeated multiplication.
In the example given, $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ can be simplified to $2^6$. Instead of writing out a long line of multiplications, we use exponent notation to make the expression simpler.

Identify repeated factors.
Use exponentiation for repeated multiplication.

This simplification makes calculations more manageable and expressions easier to read and interpret.

Basic Arithmetic Operations

Arithmetic operations form the foundation of mathematics. They include addition, subtraction, multiplication, and division. Exponentiation is an extension of multiplication, where instead of repeated addition, we repeat multiplication.
The basic operation under discussion - multiplication - is the arithmetic operation we use in exponentiation. For instance, in our exercise, multiplying 2 by itself repeatedly leads to the expression $2^6$.

Understand that multiplication is repeated addition.
Exponentiation is repeated multiplication.
Exponents help streamline complex multiplication problems.

By mastering these basic operations, complex problems become easier to tackle, and solutions become more efficient.

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91影视

\(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2\)

Short Answer

Step by step solution

Understanding the Problem

Applying the Rule of Exponentiation

Solving the Problem

Key Concepts

Powers of Numbers

Simplifying Expressions

Basic Arithmetic Operations

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