Evaluate: `(0.8 xx 0.8 xx 0.8 + 0.5 xx 0.5 xx 0.5)/(0.8 xx 0.8 - 0.8 xx 0.5 + 0.5 xx 0.5)`

Answer

To evaluate the expression \((0.8 \times 0.8 \times 0.8 + 0.5 \times 0.5 \times 0.5) / (0.8 \times 0.8 - 0.8 \times 0.5 + 0.5 \times 0.5)\), we can follow these steps:

### Step 1: Substitute Variables
Let \( A = 0.8 \) and \( B = 0.5 \). This simplifies our expression to:
\[ \frac{A^3 + B^3}{A^2 - AB + B^2} \]

### Step 2: Apply the Identity for \( A^3 + B^3 \)
We know that \( A^3 + B^3 \) can be factored using the identity:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]
Using this identity, we can rewrite our expression:
\[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 - AB + B^2} \]

### Step 3: Cancel the Common Terms
Since \( A^2 - AB + B^2 \) appears in both the numerator and the denominator, we can cancel it out (as long as it is not zero):
\[ A + B \]

### Step 4: Substitute Back the Values
Now substitute back the values of \( A \) and \( B \):
\[ A + B = 0.8 + 0.5 = 1.3 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{1.3} \]

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