Problem 33 Write in exponential form. \(x... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 2: Problem 33

Write in exponential form. $x \cdot x \cdot x \cdot x \cdot x$

Short Answer

Expert verified

x^5

Step by step solution

Identify the Base

First, identify the base of the repeated multiplication. Here, the base is the variable $x$.

Count the Number of Factors

Next, count how many times the base $x$ is being multiplied by itself. There are 5 factors of $x$.

Write in Exponential Form

Combine the base and the exponent to write the expression in exponential form. Since $x$ is multiplied by itself 5 times, it can be written as $x^5$.

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Key Concepts

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

Base

In mathematics, the base is the number or variable that is being multiplied multiple times in an expression written in exponential form. Understanding the base is crucial because it tells you what number or variable is being raised to a power.

Let's take an example from the exercise:

The expression is: $x \times x \times x \times x \times x$.
Here, the base is clearly the variable $x$ because it is the number that is being repeatedly multiplied.

Recognizing the base helps in simplifying and working with exponential expressions. In our example, the base $x$ is the foundational element of the expression.

Exponent

The exponent in an exponential expression indicates how many times the base is multiplied by itself. It's written as a small number above and to the right of the base. Understanding exponents makes it easier to handle large numbers and manage repetitive multiplication.

Applying this to our example:

To determine the exponent, count the number of times the base $x$ appears: it's 5 times.

So, the exponent here is 5. Thus, the exponential form for our example is $x^5$. The exponent tells us the depth of the repeated multiplication without having to rewrite the base multiple times.

Repeated Multiplication

Repeated multiplication refers to multiplying a number or variable by itself multiple times. It forms the basis of understanding exponential expressions.

For the expression $x \times x \times x \times x \times x$:

This can be cumbersome to write out, especially with larger numbers or more repetitions.
Exponential form simplifies repeated multiplication by using the base and the exponent.

In our example, writing out$x^5$ is far more concise and manageable. It captures the essence of multiplying $x$ by itself five times, making calculations and understanding more efficient. This concept is fundamental to algebra and higher mathematics, as it simplifies problems and reveals patterns more easily.

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91影视

Write in exponential form. \(x \cdot x \cdot x \cdot x \cdot x\)

Short Answer

Step by step solution

Identify the Base

Count the Number of Factors

Write in Exponential Form

Key Concepts

Base

Exponent

Repeated Multiplication

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