Fully simplify and write your answer in exponential form with positive exponents only. Example: 153\frac{1}{5^3}

To simplify the expression \( 13 \cdot 13 \cdot 13 \cdot 13 \cdot \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \), we first group the terms.

1. The first part \( 13 \cdot 13 \cdot 13 \cdot 13 \) can be rewritten using exponents:
\[
13^4
\]

2. The second part \( \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \) can also be rewritten using exponents:
\[
\left(\frac{1}{3}\right)^4 = \frac{1^4}{3^4} = \frac{1}{3^4}
\]

3. Combining these two simplified parts:
\[
13^4 \cdot \frac{1}{3^4} = \frac{13^4}{3^4}
\]

4. Finally, this can be expressed in exponential form:
\[
\left(\frac{13}{3}\right)^4
\]

Thus, the fully simplified result is:
\[
\left(\frac{13}{3}\right)^4
\]