The value of `(0.2xx0.2xx0.2+0.3xx0.3xx0.3)/(0.4xx0.4xx0.4+0.6xx0.6xx0.6)` is

Options

A. `1/8`
B. `1/6`
C. `1/4`
D. `1/5`

Answer

To solve the expression \((0.2 \times 0.2 \times 0.2 + 0.3 \times 0.3 \times 0.3) / (0.4 \times 0.4 \times 0.4 + 0.6 \times 0.6 \times 0.6)\), we can follow these steps:

### Step 1: Simplify the Numerator
The numerator is \(0.2 \times 0.2 \times 0.2 + 0.3 \times 0.3 \times 0.3\).

Calculating each term:
- \(0.2 \times 0.2 \times 0.2 = 0.2^3 = 0.008\)
- \(0.3 \times 0.3 \times 0.3 = 0.3^3 = 0.027\)

Now, add these two results together:
\[ 0.008 + 0.027 = 0.035 \]

### Step 2: Simplify the Denominator
The denominator is \(0.4 \times 0.4 \times 0.4 + 0.6 \times 0.6 \times 0.6\).

Calculating each term:
- \(0.4 \times 0.4 \times 0.4 = 0.4^3 = 0.064\)
- \(0.6 \times 0.6 \times 0.6 = 0.6^3 = 0.216\)

Now, add these two results together:
\[ 0.064 + 0.216 = 0.280 \]

### Step 3: Divide the Numerator by the Denominator
Now we have:
\[ \frac{0.035}{0.280} \]

To simplify this fraction, we can divide both the numerator and the denominator by \(0.035\):
\[ \frac{0.035 \div 0.035}{0.280 \div 0.035} = \frac{1}{8} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{1}{8} \]

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