Assertion : `(2)^(-3) div (2)^(-3) = (2)^(0)`
Reason : `x^(-m) div x^(-n) = x^(-mn)`

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 given assertion and reason, let's break it down step by step.

### Step 1: Understand the Assertion
The assertion states that:
\[ (2)^{-3} \div (2)^{-3} = (2)^{0} \]

### Step 2: Apply the Division Rule for Exponents
When dividing two powers with the same base, we subtract the exponents:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In our case, we have:
\[ (2)^{-3} \div (2)^{-3} = (2)^{-3 - (-3)} = (2)^{-3 + 3} = (2)^{0} \]

### Step 3: Simplify the Exponent
Now, since \(-3 + 3 = 0\), we can conclude that:
\[ (2)^{0} = 1 \]
Thus, the assertion is true.

### Step 4: Understand the Reason
The reason provided is:
\[ x^{-m} \div x^{-n} = x^{-mn} \]
However, this is incorrect. The correct formula should be:
\[ x^{-m} \div x^{-n} = x^{-m - (-n)} = x^{-m + n} \]
This means that the reason is false.

### Conclusion
- The assertion is true: \((2)^{-3} \div (2)^{-3} = (2)^{0}\).
- The reason is false: \(x^{-m} \div x^{-n} \neq x^{-mn}\).

### Final Answer
- **Assertion**: True
- **Reason**: False

---