Problem 32 Write in exponential form. 4\(... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 2: Problem 32

Write in exponential form. 4$\cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$

Short Answer

Expert verified

4^6

Step by step solution

Identify the Base

Examine the repeated multiplication. The number that is repeatedly multiplied is called the base. Here, the number 4 is the base.

Count the Number of Factors

Determine how many times the base is multiplied by itself. In this case, the number 4 is multiplied by itself 6 times.

Write in Exponential Form

Use exponential notation to express the repeated multiplication. The base is written first, followed by an exponent that shows how many times the base is multiplied by itself. So, the exponential form of the expression is 4^6. In LaTeX, it is written as: $4^6$.

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Key Concepts

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

Base and Exponent

Understanding the terms 'base' and 'exponent' is crucial when dealing with exponential form.
The base is the number you are multiplying. In our example, it is 4.
The exponent is the small number written to the upper right of the base. It shows how many times the base is used as a factor.
In the expression 4⁶, 4 is the base and 6 is the exponent.

To identify these parts:

Look at the repeated multiplication.
The base is the number being repeatedly multiplied (4).
The exponent counts how many times the base is used (6).

Repeated Multiplication

Repeated multiplication is a simple way to understand how exponential notation works.
If you multiply a number by itself multiple times, you are using repeated multiplication.
For example, 4 x 4 x 4 x 4 x 4 x 4 is repeated multiplication.

To convert this to exponential form, note:

The base (4) is the number repeatedly multiplied.
Count how many times the base is multiplied (6 times).

This makes the exponential form 4⁶.

In general, any repeated multiplication can be converted to an exponential expression to make it simpler.

Exponential Notation

Exponential notation is a shorthand way to represent repeated multiplication.
Instead of writing out a long string of multiplications, you use a base and an exponent.
For example, instead of writing 4 x 4 x 4 x 4 x 4 x 4, you write 4⁶.

This saves space and makes calculations easier:

Exponential form makes it clear that you multiply the base by itself as many times as indicated by the exponent.
It also helps in performing more complex operations, like adding and multiplying exponential expressions.

In mathematics, exponential notation is a powerful tool for simplifying expressions.

To write in exponential form, just identify the base and the number of times it's multiplied (exponent), then combine them.

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91影视

Write in exponential form. 4\(\cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\)

Short Answer

Step by step solution

Identify the Base

Count the Number of Factors

Write in Exponential Form

Key Concepts

Base and Exponent

Repeated Multiplication

Exponential Notation

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