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

To simplify the expression \( \frac{1}{z^{8}} \cdot \frac{1}{z^{7}} \), we can combine the fractions:

\[
\frac{1}{z^{8}} \cdot \frac{1}{z^{7}} = \frac{1 \cdot 1}{z^{8} \cdot z^{7}} = \frac{1}{z^{8 + 7}} = \frac{1}{z^{15}}.
\]

Next, to express this in exponential form with positive exponents only, we can rewrite \( \frac{1}{z^{15}} \) as:

\[
z^{-15}.
\]

If we need to express this with positive exponents according to the prompt's instructions, we leave it in the form \(\frac{1}{z^{15}}\).

However, since the answer must be presented with positive exponents, we don't need to change it; thus, the answer is:

\[
\frac{1}{z^{15}}.
\]