Answered

a) Simplify the expression:
[tex]\[ \left[+\frac{2}{7} \cdot 4 \times 3\right] : \left[+\frac{4}{7} \cdot x^2\right] \][/tex]



Answer :

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]