What is the simplified value of `((2.7)^3+(1.3)^3)/((2.7)^2-2.7 xx 1.3 +(1.3)^2) = ?`

Options

A. 4
B. 1.4
C. 1.3
D. 2.7

Answer

To simplify the expression \(\frac{(2.7)^3 + (1.3)^3}{(2.7)^2 - 2.7 \times 1.3 + (1.3)^2}\), we can follow these steps:

### Step 1: Identify Variables
Let \( A = 2.7 \) and \( B = 1.3 \). This allows us to rewrite the expression in terms of \( A \) and \( B \):
\[ \frac{A^3 + B^3}{A^2 - AB + B^2} \]

### Step 2: Use the Formula for Sum of Cubes
Recall the formula for the sum of cubes:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]
Using this formula, we can rewrite the numerator:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]

### Step 3: Substitute into the Expression
Now substitute this into our expression:
\[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 - AB + B^2} \]

### Step 4: Simplify the Expression
Since \( A^2 - AB + B^2 \) appears in both the numerator and denominator, we can cancel it out (as long as it is not zero):
\[ = A + B \]

### Step 5: Substitute Back the Values
Now substitute back the values of \( A \) and \( B \):
\[ A + B = 2.7 + 1.3 \]

### Step 6: Calculate the Final Value
Now, perform the addition:
\[ 2.7 + 1.3 = 4.0 \]

### Final Answer
Thus, the simplified value of the expression is:
\[ \boxed{4} \]