Let's break down and solve the given mathematical expression step by step:
Given expression:
[tex]\[
\begin{array}{l}
\left(2 x^2\right)(4) \\
(50) \div \left(2 x^1\right) \\
(2)+(4) \\
\frac{25}{100} \div \frac{50 x}{150}
\end{array}
\][/tex]
### Step 1: Simplify [tex]\((2x^2)(4)\)[/tex]
[tex]\[
(2x^2) \cdot 4 = 2 \cdot 4 \cdot x^2 = 8x^2
\][/tex]
### Step 2: Simplify [tex]\(50 \div (2x^1)\)[/tex]
[tex]\[
50 \div (2x) = \frac{50}{2x} = \frac{25}{x}
\][/tex]
### Step 3: Simplify [tex]\((2)+(4)\)[/tex]
[tex]\[
2 + 4 = 6
\][/tex]
### Step 4: Simplify [tex]\(\frac{25}{100} \div \frac{50x}{150}\)[/tex]
First, express the division as multiplication by the reciprocal:
[tex]\[
\frac{25}{100} \div \frac{50x}{150} = \frac{25}{100} \cdot \frac{150}{50x}
\][/tex]
Now, simplify each fraction:
[tex]\[
\frac{25}{100} = \frac{1}{4}
\][/tex]
[tex]\[
\frac{150}{50x} = \frac{150 \div 50}{50x \div 50} = \frac{3}{x}
\][/tex]
Thus:
[tex]\[
\frac{1}{4} \cdot \frac{3}{x} = \frac{3}{4x}
\][/tex]
### Combine the Results:
Summarizing all the simplified parts:
[tex]\[
(8x^2) + \left(\frac{25}{x}\right) + 6 + \left(\frac{3}{4x}\right)
\][/tex]
We need to just present the terms together since they cannot be combined into a single integer value without specifying [tex]\(x\)[/tex]:
[tex]\[
8x^2 + \frac{25}{x} + 6 + \frac{3}{4x}
\][/tex]
This is the final simplified result for the given expression.
