Use property to evaluate:
`13^(3) + (-8)^(3) + (-5)^(3)`

Answer

To evaluate the expression \( 13^3 + (-8)^3 + (-5)^3 \) using the property of cubes, we can follow these steps:

### Step 1: Identify A, B, and C
Let:
- \( A = 13 \)
- \( B = -8 \)
- \( C = -5 \)

### Step 2: Check if A + B + C = 0
Calculate \( A + B + C \):
\[ A + B + C = 13 + (-8) + (-5) = 13 - 8 - 5 = 0 \]
Since \( A + B + C = 0 \), we can use the property of cubes.

### Step 3: Use the Property of Cubes
The property states that if \( A + B + C = 0 \), then:
\[ A^3 + B^3 + C^3 = 3ABC \]
Now we can calculate \( 3ABC \).

### Step 4: Calculate ABC
Calculate \( ABC \):
\[ ABC = 13 \times (-8) \times (-5) \]
Calculating step-by-step:
1. \( 13 \times (-8) = -104 \)
2. \( -104 \times (-5) = 520 \)

Thus, \( ABC = 520 \).

### Step 5: Calculate \( 3ABC \)
Now we can find \( 3ABC \):
\[ 3ABC = 3 \times 520 = 1560 \]

### Final Result
Therefore, the value of \( 13^3 + (-8)^3 + (-5)^3 \) is:
\[ \boxed{1560} \]

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