If ` a = - 7, b = 5 and c= 2 ` then find the value of ` a^(3) + b^(3) + c^(3)` .

Options

A. A)`-210`
B. B)`-180`
C. C)180
D. D)210

Answer

To solve the problem, we need to find the value of \( a^3 + b^3 + c^3 \) given that \( a = -7 \), \( b = 5 \), and \( c = 2 \).

### Step-by-step Solution:

1. **Substitute the values of a, b, and c into the expression**:
\[ a^3 + b^3 + c^3 = (-7)^3 + (5)^3 + (2)^3 \]

**Hint**: Always start by substituting the given values into the expression.

2. **Calculate \( (-7)^3 \)**:
\[ (-7)^3 = -7 \times -7 \times -7 = -343 \]

**Hint**: Remember that a negative number raised to an odd power remains negative.

3. **Calculate \( (5)^3 \)**:
\[ (5)^3 = 5 \times 5 \times 5 = 125 \]

**Hint**: For positive numbers, the cube will always be positive.

4. **Calculate \( (2)^3 \)**:
\[ (2)^3 = 2 \times 2 \times 2 = 8 \]

**Hint**: Similar to the previous step, the cube of a positive number is positive.

5. **Combine all the results**:
\[ a^3 + b^3 + c^3 = -343 + 125 + 8 \]

**Hint**: When combining numbers, keep track of the signs (positive and negative).

6. **Perform the addition**:
- First, add \( 125 + 8 = 133 \)
- Then, add \( -343 + 133 = -210 \)

**Hint**: When adding a negative number to a positive number, subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value.

7. **Final Result**:
\[ a^3 + b^3 + c^3 = -210 \]

### Conclusion:
The value of \( a^3 + b^3 + c^3 \) is \( -210 \).