Sure, let's solve the given expression step by step.
The given expression is:
[tex]\[
\left[ \frac{2}{7} a \cdot 4 \cdot 3 \right] : \left[ \frac{4}{7} a x^2 \right]
\][/tex]
### Step 1: Simplify the Numerator and the Denominator Separately
First, simplify the numerator:
[tex]\[
\frac{2}{7} a \cdot 4 \cdot 3
\][/tex]
Combine constants:
[tex]\[
\frac{2 \times 4 \times 3}{7}a
\][/tex]
This simplifies to:
[tex]\[
\frac{24}{7}a = 3.42857142857143a
\][/tex]
Now, simplify the denominator:
[tex]\[
\frac{4}{7} a x^2
\][/tex]
Combine terms:
[tex]\[
\frac{4}{7}a x^2
\][/tex]
### Step 2: Setup Division of the Simplified Expressions
Now, we need to divide the simplified numerator by the simplified denominator:
[tex]\[
\frac{\left( \frac{24}{7}a \right)}{\left( \frac{4}{7}a x^2 \right)}
\][/tex]
### Step 3: Simplify the Fraction
To simplify this, we multiply by the reciprocal of the denominator:
[tex]\[
\left( \frac{24}{7}a \right) \times \left( \frac{7}{4ax^2} \right)
\][/tex]
### Step 4: Cancel Out Common Factors
Notice that [tex]\(a\)[/tex] can be canceled (assuming [tex]\(a \neq 0\)[/tex]):
[tex]\[
\frac{24}{7} \times \frac{7}{4x^2}
\][/tex]
[tex]\[
= \frac{24 \cdot 7}{7 \cdot 4 x^2}
\][/tex]
### Step 5: Simplify the Remaining Expression
Cancel the common factor of 7 in the numerator and the denominator:
[tex]\[
\frac{24}{4x^2} = \frac{6}{x^2}
\][/tex]
### Final Answer:
[tex]\[
\frac{6}{x^2}
\][/tex]
So, the final result of the given expression is:
[tex]\[
\boxed{\frac{6}{x^2}}
\][/tex]
