The value of following is:
`(0.2xx0.02xx0.002xx32)/(0.4xx0.04xx0.004xx16)`

Options

A. `0.40`
B. `0.20`
C. `0.25`
D. `0.50`

Answer

To solve the expression \((0.2 \times 0.02 \times 0.002 \times 32) / (0.4 \times 0.04 \times 0.004 \times 16)\), we will break it down step by step.

### Step 1: Simplify the Numerator
First, we will calculate the numerator:
\[ 0.2 \times 0.02 \times 0.002 \times 32 \]
We can express the decimal numbers as fractions:
\[ 0.2 = \frac{2}{10}, \quad 0.02 = \frac{2}{100}, \quad 0.002 = \frac{2}{1000} \]
Thus, we have:
\[ 0.2 \times 0.02 \times 0.002 = \frac{2}{10} \times \frac{2}{100} \times \frac{2}{1000} = \frac{2 \times 2 \times 2}{10 \times 100 \times 1000} = \frac{8}{1000000} \]
Now, multiplying by 32:
\[ \frac{8}{1000000} \times 32 = \frac{256}{1000000} \]

### Step 2: Simplify the Denominator
Next, we calculate the denominator:
\[ 0.4 \times 0.04 \times 0.004 \times 16 \]
Again, we can express the decimal numbers as fractions:
\[ 0.4 = \frac{4}{10}, \quad 0.04 = \frac{4}{100}, \quad 0.004 = \frac{4}{1000} \]
Thus, we have:
\[ 0.4 \times 0.04 \times 0.004 = \frac{4}{10} \times \frac{4}{100} \times \frac{4}{1000} = \frac{4 \times 4 \times 4}{10 \times 100 \times 1000} = \frac{64}{1000000} \]
Now, multiplying by 16:
\[ \frac{64}{1000000} \times 16 = \frac{1024}{1000000} \]

### Step 3: Form the Final Expression
Now we can form the final expression:
\[ \frac{\frac{256}{1000000}}{\frac{1024}{1000000}} = \frac{256}{1024} \]

### Step 4: Simplify the Fraction
Now we simplify \(\frac{256}{1024}\):
\[ \frac{256}{1024} = \frac{1}{4} \]

### Step 5: Convert to Decimal
Finally, converting \(\frac{1}{4}\) to decimal gives us:
\[ \frac{1}{4} = 0.25 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{0.25} \]