Use the product notation to rewrite the following expression.\[(t - 4) \cdot (t^2 - 4) \cdot (t^3 - 4) \cdot (t^4 - 4) \cdot (t^5 - 4) \cdot (t^6 - 4) = \prod_{k=1}^{6} (t^k - 4)\]Explanation of Notation:The symbol $\prod$ represents the product notation, analogous to summation notation (denoted by $\sum$), but for products. In this case, it indicates that you need to multiply a sequence of expressions together.- The lower bound $k = 1$ and upper bound $6$ signify that the variable $k$ starts at 1 and ends at 6.- Each term inside the product is of the form $t^k - 4$, where $k$ takes on integer values from 1 to 6.- This notation succinctly represents the same expression as the expanded product of terms shown before the equation.

Given expression:To define:Corresponding product notation

Answered: Use the product notation to rewrite the…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Use the product notation to rewrite the following expression.

\[
(t - 4) \cdot (t^2 - 4) \cdot (t^3 - 4) \cdot (t^4 - 4) \cdot (t^5 - 4) \cdot (t^6 - 4) = \prod_{k=1}^{6} (t^k - 4)
\]

Explanation of Notation:

The symbol $\prod$ represents the product notation, analogous to summation notation (denoted by $\sum$), but for products. In this case, it indicates that you need to multiply a sequence of expressions together.

- The lower bound $k = 1$ and upper bound $6$ signify that the variable $k$ starts at 1 and ends at 6.
- Each term inside the product is of the form $t^k - 4$, where $k$ takes on integer values from 1 to 6.
- This notation succinctly represents the same expression as the expanded product of terms shown before the equation.

Expert Solution

Step 1: Defining the given data and objective

Given expression:

$left parenthesis t to the power of blank minus 4 right parenthesis. left parenthesis t squared minus 4 right parenthesis. left parenthesis t cubed minus 4 right parenthesis. left parenthesis t to the power of 4 minus 4 right parenthesis. left parenthesis t to the power of 5 minus 4 right parenthesis. left parenthesis t to the power of 6 minus 4 right parenthesis$

To define:

Corresponding product notation

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