To rewrite the expression \(3 - \left(\frac{17}{8}\right)^{-14}\) using only positive exponents, we first need to focus on the term with the negative exponent.
The property of negative exponents states that:
\[ a^{-n} = \frac{1}{a^n} \]
Applying this to \(\left(\frac{17}{8}\right)^{-14}\):
\[ \left(\frac{17}{8}\right)^{-14} = \frac{1}{\left(\frac{17}{8}\right)^{14}} \]
Therefore, the expression \(3 - \left(\frac{17}{8}\right)^{-14}\) can be rewritten as:
\[ 3 - \frac{1}{\left(\frac{17}{8}\right)^{14}} \]
Next, we can calculate \(\left(\frac{17}{8}\right)^{14}\):
\[ \left(\frac{17}{8}\right)^{14} = \frac{17^{14}}{8^{14}} \]
This means the expression can further be rewritten as:
\[ 3 - \frac{1}{\frac{17^{14}}{8^{14}}} = 3 - \frac{8^{14}}{17^{14}} \]
Overall, the expression \(3 - \left(\frac{17}{8}\right)^{-14}\) with all positive exponents can be expressed as:
\[ 3 - \frac{8^{14}}{17^{14}} \]
This is the final expression with positive exponents only.
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