91Ó°ÊÓ

The Multiplication Rule is a fundamental concept in algebra, especially when dealing with exponents. It states that when you multiply two expressions with the same base, you can simply add the exponents together. Consider the example from our exercise where we have

• \(b^3 * b\)

Here, both terms share the base \(b\).
By applying the multiplication rule, we add the exponents: \(3 + 1\).
This gives us \(b^4\).
It's important to remember that this rule only applies when the bases are identical; otherwise, you cannot combine the exponents in such a way.

A simplified expression is one that has been reduced to the simplest possible form, with no further operations that can make it shorter or clearer. In the context of the exercise, after breaking down the initial expression and applying the multiplication rule, we obtain

• \(27*b^4\)

This is our simplified expression.
Originally, we had an expression:

• \((3b)^{3} \cdot b\),

which involved multiple terms and operations, but through systematic reduction, it has been converted to a form that is concise and easy to understand.

Algebraic expressions consist of numbers, variables, and operations, forming a sort of mathematical phrase that's key in algebra. In our exercise,

• \((3b)^{3} \cdot b\)

serves as a typical algebraic expression. It includes the constant 3, the variable \(b\), and operations such as exponentiation and multiplication.
When working with algebraic expressions, it's crucial to understand the roles of different components.
Constants like the number 3 provide a fixed reference, while variables like \(b\) represent unknown values that can change.
Operations guide how these elements are combined or changed to form new expressions. Mastery of handling these components helps in efficiently solving algebraic problems.