To simplify the expression \( \frac{1}{z^6} \cdot \frac{1}{z^6} \), you can follow these steps:
1. First, rewrite the expression using the multiplication of the fractions:
\[
\frac{1}{z^6} \cdot \frac{1}{z^6} = \frac{1 \cdot 1}{z^6 \cdot z^6}
\]
2. The product of \( z^6 \cdot z^6 \) can be simplified using the property of exponents:
\[
z^6 \cdot z^6 = z^{6+6} = z^{12}
\]
3. Therefore, the expression becomes:
\[
\frac{1}{z^{12}}
\]
4. To write this with a positive exponent, you can rewrite the fraction as:
\[
z^{-12}
\]
So, the fully simplified form of your original expression \( \frac{1}{z^6} \cdot \frac{1}{z^6} \) is
\[
z^{-12}.
\]
However, since the problem asks for positive exponents only, you would typically express it as:
\[
\frac{1}{z^{12}}.
\]
Thus, the final answer in exponent form with positive exponents is:
\[
\frac{1}{z^{12}}.
\]