Let's start by analyzing the given expression: [tex]\(2b \cdot 2b \cdot 2b\)[/tex].
First, identify the repeated term in the product. In this case, we can see that the term [tex]\(2b\)[/tex] is being multiplied by itself three times.
To condense this into a single expression with an exponent, recognize that repeated multiplication of the same term can be written using exponents. Specifically, if a term [tex]\( x \)[/tex] is multiplied by itself [tex]\( n \)[/tex] times, it can be written as [tex]\( x^n \)[/tex].
Here, the term [tex]\( 2b \)[/tex] is being multiplied by itself three times, so we use an exponent of 3.
Thus, the condensed form of the expression [tex]\(2b \cdot 2b \cdot 2b\)[/tex] is:
[tex]\[ (2b)^3 \][/tex]
Let's simplify this further. In order to express this in its simplest form, we'll need to separate the factors in the base term where possible.
The term [tex]\(2b\)[/tex] consists of a constant [tex]\(2\)[/tex] and a variable [tex]\(b\)[/tex]. When raised to the power of 3, both the constant and the variable are raised to the power of 3:
[tex]\[ (2b)^3 = 2^3 \cdot b^3 = 8b^3 \][/tex]
So, the simplified form of the condensed expression [tex]\( (2b)^3 \)[/tex] is:
[tex]\[ 8b^3 \][/tex]
Thus, the final answer in condensed form with the appropriate exponent is:
[tex]\[ (2b)^3 \][/tex]
And the simplified form:
[tex]\[ 8b^3 \][/tex]
Given our task was strictly to condense the expression and enter the base and exponent form on the Answer Attempt step, here is that result formatted as required:
[tex]\[
(\boxed{2b})^3
\][/tex]
The answer is:
[tex]\[ (2b)^3 \][/tex]
