What is the value of `((0.7)^(3) + (0.3)^(3))/((0.7)^(2) - 0.7 xx 0.3 + (0.3)^(2))` ?

Options

A. 1.2
B. 0.8
C. 1
D. 1.4

Answer

To solve the expression \(\frac{(0.7)^3 + (0.3)^3}{(0.7)^2 - 0.7 \times 0.3 + (0.3)^2}\), we can use the formulas for the sum of cubes and the difference of squares.

### Step 1: Identify A and B
Let \( A = 0.7 \) and \( B = 0.3 \).

### Step 2: Apply the Sum of Cubes Formula
The sum of cubes formula states:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]
Substituting \( A \) and \( B \):
\[ (0.7)^3 + (0.3)^3 = (0.7 + 0.3)((0.7)^2 - (0.7)(0.3) + (0.3)^2) \]
Calculating \( 0.7 + 0.3 \):
\[ 0.7 + 0.3 = 1 \]
Thus, we have:
\[ (0.7)^3 + (0.3)^3 = 1 \cdot ((0.7)^2 - (0.7)(0.3) + (0.3)^2) \]

### Step 3: Substitute into the Expression
Now substituting back into the original expression:
\[ \frac{(0.7)^3 + (0.3)^3}{(0.7)^2 - 0.7 \times 0.3 + (0.3)^2} = \frac{1 \cdot ((0.7)^2 - (0.7)(0.3) + (0.3)^2)}{(0.7)^2 - 0.7 \times 0.3 + (0.3)^2} \]

### Step 4: Simplify the Expression
Since the numerator and denominator are the same, we can simplify:
\[ \frac{(0.7)^2 - 0.7 \times 0.3 + (0.3)^2}{(0.7)^2 - 0.7 \times 0.3 + (0.3)^2} = 1 \]

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