For any two non zero rational numbers x and `y, x^(4)-:y^(4)` is equal to

Options

A. `(x-:y)^(0)`
B. `(x-:y)^(1)`
C. `(x-:y)^(4)`
D. `(x-:y)^(8)`

Answer

To solve the problem, we need to simplify the expression \( \frac{x^4}{y^4} \).

### Step-by-Step Solution:

1. **Write the Expression**: Start with the expression given in the problem.
\[ \frac{x^4}{y^4} \]

2. **Use the Property of Exponents**: We can apply the property of exponents which states that \( \frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m \). Here, \( a = x \), \( b = y \), and \( m = 4 \).
\[ \frac{x^4}{y^4} = \left(\frac{x}{y}\right)^4 \]

3. **Final Expression**: Thus, we can conclude that:
\[ \frac{x^4}{y^4} = \left(\frac{x}{y}\right)^4 \]

### Conclusion:
The expression \( \frac{x^4}{y^4} \) is equal to \( \left(\frac{x}{y}\right)^4 \).

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