What will come in place of the question mark(?) in the following questions ? (a,b,c are integers)
`(a)^c xx(b)^c xx?=0`

Options

A. 1
B. -1
C. 0
D. `(c)^b`

Answer

To solve the equation \((a)^c \times (b)^c \times ? = 0\), we need to determine what value can replace the question mark (?) so that the entire expression equals zero.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation we have is \((a)^c \times (b)^c \times ? = 0\). This means that the product of these three terms must equal zero.

2. **Using the Zero Product Property**:
According to the zero product property, if the product of several factors equals zero, at least one of the factors must be zero. Therefore, we can analyze the factors:
- \((a)^c\)
- \((b)^c\)
- ?

3. **Identifying Conditions for Zero**:
For the product to equal zero, at least one of the following must be true:
- \((a)^c = 0\)
- \((b)^c = 0\)
- ? = 0

4. **Analyzing the Factors**:
- If \((a)^c = 0\), then \(a\) must be zero (since any non-zero integer raised to any power is non-zero).
- If \((b)^c = 0\), then \(b\) must also be zero.
- If neither \(a\) nor \(b\) is zero, then the only way for the product to equal zero is for ? to be zero.

5. **Conclusion**:
Since we want the product to equal zero regardless of the values of \(a\) and \(b\), the simplest solution is to set ? equal to zero. Thus, we have:
\[ ? = 0 \]

### Final Answer:
The value that comes in place of the question mark (?) is **0**.

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