Alright, let's break this down step-by-step.
### Step 1: Simplifying the Expression [tex]\((3x^2)^0\)[/tex]
We need to determine the value of [tex]\((3x^2)^0\)[/tex] given that [tex]\(x \neq 0\)[/tex].
Rule: Any non-zero number raised to the power of 0 is equal to 1.
Thus:
[tex]\[
(3x^2)^0 = 1
\][/tex]
### Step 2: Simplifying the Product of [tex]\(x\)[/tex]'s
The expression [tex]\(x \cdot x \cdot x \cdot x \cdot x\)[/tex] involves multiplying the variable [tex]\(x\)[/tex] by itself several times.
Simplification:
[tex]\[
x \cdot x \cdot x \cdot x \cdot x = x^5
\][/tex]
### Combining Both Steps
We have two results from the above steps:
1. [tex]\((3x^2)^0 = 1\)[/tex]
2. [tex]\(x \cdot x \cdot x \cdot x \cdot x = x^5\)[/tex]
These results can be summarized as follows:
[tex]\[
\left(3x^2\right)^0 = 1 \quad \text{and} \quad x \cdot x \cdot x \cdot x \cdot x = x^5
\][/tex]
Therefore, the respective results for the given expressions are [tex]\(1\)[/tex] and [tex]\(x^5\)[/tex].
I hope this detailed breakdown clarifies the solution for you! Keep practicing, and don't hesitate to ask more questions if you have any.
