Where `x ^(m)` is multiplied by `x ^(n)` product is 1. The relation between m and n is :

Options

A. `m=n`
B. `m=-n `
C. `m n = 1`
D. `m + n =1`

Answer

To solve the problem where \( x^m \) multiplied by \( x^n \) equals 1, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**: We know that when \( x^m \) is multiplied by \( x^n \), the product is 1. This can be expressed mathematically as:
\[ x^m \cdot x^n = 1 \]

2. **Use the Property of Exponents**: According to the laws of exponents, when we multiply two expressions with the same base, we add their exponents:
\[ x^{m+n} = 1 \]

3. **Identify When the Expression Equals 1**: The expression \( x^{m+n} = 1 \) holds true when the exponent \( m+n \) is equal to 0 (assuming \( x \neq 0 \)):
\[ m + n = 0 \]

4. **Solve for the Relationship Between m and n**: Rearranging the equation \( m + n = 0 \) gives us:
\[ m = -n \]

### Conclusion:
The relation between \( m \) and \( n \) is:
\[ m = -n \]