The value of `(0.1xx0.1xx0.1+0.02xx0.02xx0.02)/(0.4xx0.4xx0.4+0.08xx0.08xx0.08)`is

Options

A. `1/4`
B. `1/16`
C. `1/64`
D. `1/72`

Answer

To solve the expression \((0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02) / (0.4 \times 0.4 \times 0.4 + 0.08 \times 0.08 \times 0.08)\), we can follow these steps:

### Step 1: Calculate the numerator
The numerator is \(0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02\).

- Calculate \(0.1 \times 0.1 \times 0.1\):
\[ 0.1 \times 0.1 = 0.01 \]
\[ 0.01 \times 0.1 = 0.001 \]
So, \(0.1^3 = 0.001\).

- Calculate \(0.02 \times 0.02 \times 0.02\):
\[ 0.02 \times 0.02 = 0.0004 \]
\[ 0.0004 \times 0.02 = 0.000008 \]
So, \(0.02^3 = 0.000008\).

Now, add these two results:
\[ 0.001 + 0.000008 = 0.001008 \]

### Step 2: Calculate the denominator
The denominator is \(0.4 \times 0.4 \times 0.4 + 0.08 \times 0.08 \times 0.08\).

- Calculate \(0.4 \times 0.4 \times 0.4\):
\[ 0.4 \times 0.4 = 0.16 \]
\[ 0.16 \times 0.4 = 0.064 \]
So, \(0.4^3 = 0.064\).

- Calculate \(0.08 \times 0.08 \times 0.08\):
\[ 0.08 \times 0.08 = 0.0064 \]
\[ 0.0064 \times 0.08 = 0.000512 \]
So, \(0.08^3 = 0.000512\).

Now, add these two results:
\[ 0.064 + 0.000512 = 0.064512 \]

### Step 3: Divide the results from Step 1 and Step 2
Now we divide the numerator by the denominator:
\[ \frac{0.001008}{0.064512} \]

To simplify this, we can convert both numbers into fractions:
\[ 0.001008 = \frac{1008}{1000000}, \quad 0.064512 = \frac{64512}{1000000} \]
So, we have:
\[ \frac{1008}{64512} \]

### Step 4: Simplify the fraction
Now, simplify \(\frac{1008}{64512}\):
\[ \frac{1008 \div 1008}{64512 \div 1008} = \frac{1}{64} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{1}{64} \]