`(3 ^(-6) xx 3 ^(4)) = ? `

Options

A. `3 ^(-2)`
B. `3 ^(2)`
C. `3 ^(-10)`
D. `3 ^(10)`

Answer

To solve the expression \( (3^{-6} \times 3^{4}) \), we can use the property of exponents that states:

\[ a^m \times a^n = a^{m+n} \]

### Step-by-Step Solution:

1. **Identify the Base and Exponents**:
- The base is \( 3 \).
- The exponents are \( -6 \) and \( 4 \).

2. **Apply the Exponent Rule**:
- Since the bases are the same, we can add the exponents:
\[ 3^{-6} \times 3^{4} = 3^{-6 + 4} \]

3. **Calculate the Exponent**:
- Now, simplify the exponent:
\[ -6 + 4 = -2 \]
- Therefore, we have:
\[ 3^{-2} \]

4. **Final Result**:
- The simplified expression is:
\[ 3^{-2} \]

### Conclusion:
The answer to the expression \( (3^{-6} \times 3^{4}) \) is \( 3^{-2} \).