What will come in place of the question mark (?) in the following questions ? (a,b,c are integers)
`[(a)^2]? = a^6`

Options

A. 6
B. 5
C. `(a)^4`
D. 2a

Answer

To solve the equation \((a^2)^{?} = a^6\), we will use the properties of exponents.

### Step-by-step Solution:

1. **Understand the equation**: We have \((a^2)^{?} = a^6\). This means we need to find the value of \(?\) that makes this equation true.

2. **Apply the power of a power rule**: According to the exponent rules, \((x^m)^n = x^{m \cdot n}\). Therefore, we can rewrite the left side of the equation:
\[ (a^2)^{?} = a^{2 \cdot ?} \]

3. **Set the exponents equal**: Since the bases are the same (both sides are powers of \(a\)), we can set the exponents equal to each other:
\[ 2 \cdot ? = 6 \]

4. **Solve for \(?\)**: To find \(?\), divide both sides of the equation by 2:
\[ ? = \frac{6}{2} = 3 \]

5. **Conclusion**: The value that comes in place of the question mark is \(3\).

### Final Answer:
The value of \(?\) is \(3\).