`a^(m)xxa^(n)` is equal to

Options

A. `(a^(2))^(mn)`
B. `a^(m-n)`
C. `a^(m+n)`
D. `a^(mn)`

Answer

To solve the expression \( a^m \times a^n \), we can use the property of exponents that states when multiplying two powers with the same base, we can add their exponents.

Here’s the step-by-step solution:

1. **Identify the bases and exponents**: In the expression \( a^m \times a^n \), the base is \( a \) and the exponents are \( m \) and \( n \).

2. **Apply the property of exponents**: According to the property of exponents, when multiplying two powers with the same base, we add the exponents. This can be written as:
\[ a^m \times a^n = a^{m+n} \]

3. **Write the final answer**: Therefore, the expression \( a^m \times a^n \) simplifies to:
\[ a^{m+n} \]

### Final Answer:
\[ a^m \times a^n = a^{m+n} \]