To simplify the expression \((\frac{7}{8})^7 \cdot 7^2\), we can rewrite \(\frac{7}{8}\) in a way that separates the base \(7\) from the base \(8\).
\[ \left(\frac{7}{8}\right)^{7} = \frac{7^7}{8^7} \]
Now, substitute this into the expression:
\[ \frac{7^7}{8^7} \cdot 7^2 \]
Next, we can combine the \(7\) terms in the numerator:
\[ \frac{7^{7} \cdot 7^{2}}{8^7} \]
Using the power rule for exponents (\(a^m \cdot a^n = a^{m+n}\)), we combine the exponents of \(7\):
\[ \frac{7^{7+2}}{8^7} = \frac{7^9}{8^7} \]
Thus, the simplified expression in exponential form is:
\[ \frac{7^9}{8^7} \]