To simplify the expression \(\frac{1}{z^7} \cdot \frac{1}{z^7}\), we start by multiplying the two fractions:
\[ \frac{1}{z^7} \cdot \frac{1}{z^7} = \frac{1 \cdot 1}{z^7 \cdot z^7} = \frac{1}{z^{7 + 7}} = \frac{1}{z^{14}}. \]
Next, we can express this in exponential form. Since \(\frac{1}{z^{14}} = z^{-14}\), we write:
\[ z^{-14}. \]
To ensure the exponent is positive, we can represent this expression in a format with positive exponents only:
\[ \frac{1}{z^{14}}. \]
Thus, the fully simplified answer in exponential form with positive exponents is:
\[ \frac{1}{z^{14}}. \]