`(-7)^(5)xx(-7)^(3)` is equal to

Options

A. `(-7)^(8)`
B. `-(7)^(8)`
C. `(-7)^(15)`
D. `(-7)^(2)`

Answer

To solve the expression \((-7)^{5} \times (-7)^{3}\), we can use the property of exponents that states:

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

where \(a\) is the base and \(m\) and \(n\) are the exponents.

### Step-by-Step Solution:

1. **Identify the bases and exponents**:
- Here, the base \(a\) is \(-7\), and the exponents are \(5\) and \(3\).

2. **Apply the exponent multiplication property**:
- According to the property mentioned, we can add the exponents since the bases are the same:
\[ (-7)^{5} \times (-7)^{3} = (-7)^{5+3} \]

3. **Calculate the sum of the exponents**:
- Now, we add the exponents:
\[ 5 + 3 = 8 \]

4. **Write the final expression**:
- Therefore, we have:
\[ (-7)^{5} \times (-7)^{3} = (-7)^{8} \]

5. **Conclusion**:
- The expression \((-7)^{5} \times (-7)^{3}\) simplifies to \((-7)^{8}\).

### Final Answer:
\[ (-7)^{8} \]