Express each of the following in exponential notation:
` ((13)/( 43))^(7) xx ( ( 13)/( 43))`

Answer

To express the given expression \(\left(\frac{13}{43}\right)^{7} \times \left(\frac{13}{43}\right)\) in exponential notation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Base and Powers**:
The base here is \(\frac{13}{43}\). The first term has a power of 7, and the second term is \(\frac{13}{43}\) which can be considered as having an implicit power of 1.

\[ \text{Base} = \frac{13}{43}, \quad \text{First Power} = 7, \quad \text{Second Power} = 1 \]

2. **Apply the Exponent Multiplication Rule**:
According to the exponent rule \(a^m \times a^n = a^{m+n}\), we can add the exponents when the bases are the same.

\[ \left(\frac{13}{43}\right)^{7} \times \left(\frac{13}{43}\right)^{1} = \left(\frac{13}{43}\right)^{7+1} \]

3. **Calculate the New Exponent**:
Now, we simply add the exponents:

\[ 7 + 1 = 8 \]

4. **Write the Final Expression**:
Therefore, we can express the original expression in exponential notation as:

\[ \left(\frac{13}{43}\right)^{8} \]

### Final Answer:
\[ \left(\frac{13}{43}\right)^{8} \]