Assertion : `((5)/(7))^(0) = 1`
Reason : For any non-zero rational number `x, x^(0) = 1`

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the assertion and reason provided in the question, we will analyze both statements step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that \(\left(\frac{5}{7}\right)^{0} = 1\).

2. **Understanding the Reason**:
The reason given is that for any non-zero rational number \(x\), \(x^{0} = 1\).

3. **Applying the Reason to the Assertion**:
We need to check if \(\frac{5}{7}\) is a non-zero rational number. Since both 5 and 7 are non-zero integers, \(\frac{5}{7}\) is indeed a non-zero rational number.

4. **Using the Exponent Rule**:
According to the exponent rule, any non-zero number raised to the power of 0 is equal to 1. Therefore, since \(\frac{5}{7}\) is a non-zero rational number, we can apply this rule:
\[ \left(\frac{5}{7}\right)^{0} = 1 \]

5. **Conclusion**:
Since both the assertion and the reason are true, we conclude that the assertion \(\left(\frac{5}{7}\right)^{0} = 1\) is correct, and the reason provided correctly explains why it is true.

### Final Statement:
Both the assertion and the reason are correct, and the reason is the correct explanation for the assertion.

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