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

Answer

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

### Step 1: Identify the values of \(x\), \(y\), and \(z\)
Let:
- \(x = 8\)
- \(y = -5\)
- \(z = -3\)

### Step 2: Check if \(x + y + z = 0\)
Calculate:
\[ x + y + z = 8 + (-5) + (-3) = 8 - 5 - 3 = 0 \]
Since the sum is equal to 0, we can use the property of cubes.

### Step 3: Apply the property of cubes
The property states that if \(x + y + z = 0\), then:
\[ x^3 + y^3 + z^3 = 3xyz \]
Substituting the values of \(x\), \(y\), and \(z\):
\[ 8^3 + (-5)^3 + (-3)^3 = 3 \cdot 8 \cdot (-5) \cdot (-3) \]

### Step 4: Calculate \(xyz\)
Now calculate \(xyz\):
\[ xyz = 8 \cdot (-5) \cdot (-3) \]
Calculating step by step:
1. \(8 \cdot (-5) = -40\)
2. \(-40 \cdot (-3) = 120\)

### Step 5: Multiply by 3
Now multiply by 3:
\[ 3xyz = 3 \cdot 120 = 360 \]

### Final Answer
Thus, the value of \(8^3 + (-5)^3 + (-3)^3\) is:
\[ \boxed{360} \]