To apply the property of negative integer exponents, we can use the rule that states \( a^{-n} = \frac{1}{a^n} \).
Starting with the expression:
\[ 3^{-17} \cdot 8^{-14} \]
We can convert the negative exponents to positive by applying the rule:
\[ 3^{-17} = \frac{1}{3^{17}} \] \[ 8^{-14} = \frac{1}{8^{14}} \]
Substituting these into the original expression gives:
\[ 3^{-17} \cdot 8^{-14} = \frac{1}{3^{17}} \cdot \frac{1}{8^{14}} = \frac{1}{3^{17} \cdot 8^{14}} \]
Thus, the expression \( 3^{-17} \cdot 8^{-14} \) is equivalent to:
\[ \frac{1}{3^{17} \cdot 8^{14}} \]
This expression has only positive exponents.