To simplify the expression \(\frac{3^{-17}}{8^{-14}}\) and express it with positive exponents only, we can use the property of negative integer exponents, which states that \(a^{-n} = \frac{1}{a^{n}}\).
Applying this property:
\[ \frac{3^{-17}}{8^{-14}} = \frac{1}{3^{17}} \div \frac{1}{8^{14}} \]
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ \frac{1}{3^{17}} \div \frac{1}{8^{14}} = \frac{1}{3^{17}} \cdot 8^{14} = \frac{8^{14}}{3^{17}} \]
Next, we leave the expression as it is in terms of positive exponents:
\[ \frac{8^{14}}{3^{17}} \]
Now we should check if this can be simplified. However, \(8^{14}\) and \(3^{17}\) have no common factors, so the expression is already in its simplest form.
Thus, the final answer is:
\[ \frac{8^{14}}{3^{17}} \]