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Chapter 2: Problem 34

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

Short Answer

Expert verified
The exponential form is \(y^6\).

Step by step solution

01

Identify the Base

Determine the common factor that is being repeatedly multiplied. In this case, the common factor is the variable 'y'.
02

Count the Factors

Count how many times the factor 'y' appears in the product. Here, 'y' is multiplied 6 times.
03

Express in Exponential Form

Combine the base and the count of the factors using exponential notation. This product can be written as: \(y^6\)

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Key Concepts

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

Exponents
An exponent is a mathematical notation indicating the number of times a number or variable is multiplied by itself. When you see an expression like \(y^6\), the number 6 is the exponent. This shows that the base, which is 'y' in this case, is multiplied by itself 6 times. Exponents are a concise way to express repeated multiplication, making long multiplication expressions simpler and more manageable to write and comprehend.
Base and Exponent
In exponential notation, there are two main components: the base and the exponent.
The base is the number or variable that is being multiplied. For example, in the expression \(y^6\), 'y' is the base.
The exponent is the small number written to the upper right of the base. It tells you how many times the base is used as a factor in the multiplication. In \(y^6\), the exponent is 6, which means 'y' is multiplied by itself 6 times.

Understanding these two components is crucial for working with exponents and recognizing exponential forms in algebra.
Repeated Multiplication
Repeated multiplication occurs when the same number or variable is multiplied by itself multiple times. Let's break down an example:

Take the expression given in your exercise: \(y \cdot y \cdot y \cdot y \cdot y \cdot y\).
  • The variable 'y' is the number being repeatedly multiplied.
  • Count how many times 'y' appears in the expression 鈥� it鈥檚 6 times.
  • This can be written in exponential form as \(y^6\), which is much simpler and shorter to write.
Using exponential notation helps you quickly understand and manipulate expressions involving repeated multiplication. This not only makes your work look cleaner but also makes it easier to perform further mathematical operations on these expressions.

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