To rewrite the expression \( \frac{3^{-17}}{8^{-14}} \) using only positive exponents, we can apply the property of negative integer exponents, which states that \( a^{-n} = \frac{1}{a^n} \).
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Start with the original expression: \[ \frac{3^{-17}}{8^{-14}} \]
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Apply the property of negative exponents: \[ = 3^{-17} \cdot 8^{14} \]
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Rewrite \( 3^{-17} \): \[ = \frac{8^{14}}{3^{17}} \]
So, the expression \( \frac{3^{-17}}{8^{-14}} \) with positive exponents only is: \[ \frac{8^{14}}{3^{17}} \]