If x be any non zero integer and m, n be negative integers. Then `x^(m)xxx^(n)` is equal to

Options

A. `x^(m)`
B. `x^(m+n)`
C. `x^(n)`
D. `x^(m-n)`

Answer

To solve the problem, we need to use the laws of exponents. The question asks us to simplify the expression \( x^m \cdot x^n \) where \( m \) and \( n \) are negative integers and \( x \) is a non-zero integer.

### Step-by-Step Solution:

1. **Identify the Expression**: We start with the expression \( x^m \cdot x^n \).

2. **Apply the Law of Exponents**: According to the law of exponents, when we multiply two expressions with the same base, we can add their exponents. This can be written as:
\[ a^m \cdot a^n = a^{m+n} \]
In our case, \( a \) is \( x \), so we can write:
\[ x^m \cdot x^n = x^{m+n} \]

3. **Combine the Exponents**: Since \( m \) and \( n \) are negative integers, we can express the result as:
\[ x^{m+n} \]

4. **Final Result**: Thus, the expression \( x^m \cdot x^n \) simplifies to:
\[ x^{m+n} \]

### Conclusion:
The final answer is \( x^{m+n} \).

---