If x be any integer different from zero and m, n be any integers, then `(x^(m))^(n)` is equal to

Options

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

Answer

To solve the question, we need to apply the laws of exponents. The question states that if \( x \) is any integer different from zero and \( m \) and \( n \) are any integers, then we want to find the value of \( (x^m)^n \).

### Step-by-Step Solution:

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

2. **Apply the exponent rule**: According to the laws of exponents, specifically the third law of exponents, we know that:
\[ (a^m)^n = a^{m \cdot n} \]
Here, \( a \) is replaced by \( x \).

3. **Substitute into the expression**: Applying this rule to our expression, we have:
\[ (x^m)^n = x^{m \cdot n} \]

4. **Final result**: Therefore, we can conclude that:
\[ (x^m)^n = x^{mn} \]

### Conclusion:
Thus, the expression \( (x^m)^n \) is equal to \( x^{mn} \).