To rewrite the expression \(\frac{3^{17}}{8^{14}}\) using positive exponents only, we start by recognizing that the negative exponent property states that \(a^{-n} = \frac{1}{a^n}\).
Thus, we can express \(8^{14}\) in the denominator as follows:
\[ \frac{3^{17}}{8^{14}} = 3^{17} \cdot 8^{-14} \]
Now, to further express this specifically in terms of base 2, we can note that \(8\) can be written as \(2^3\):
\[ 8^{14} = (2^3)^{14} = 2^{3 \times 14} = 2^{42} \]
So we can rewrite the expression:
\[ 8^{-14} = (2^{42})^{-1} = 2^{-42} \]
Putting this all together, we have:
\[ 3^{17} \cdot 8^{-14} = 3^{17} \cdot 2^{-42} \]
Finally, we express it entirely with positive exponents:
\[ 3^{17} \cdot \frac{1}{2^{42}} = \frac{3^{17}}{2^{42}} \]
Therefore, the expression \(\frac{3^{17}}{8^{14}}\) with positive exponents only is:
\[ \frac{3^{17}}{2^{42}} \]
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