To apply the property of negative integer exponents and convert the expression \( 3^{-17}/8^{-14} \) into an expression with positive exponents, we can use the rule that \( a^{-n} = \frac{1}{a^n} \).
Starting with the expression:
\[ \frac{3^{-17}}{8^{-14}} \]
we can rewrite it by applying the negative exponent property:
\[ 3^{-17} = \frac{1}{3^{17}} \quad \text{and} \quad 8^{-14} = \frac{1}{8^{14}} \]
Thus, we can write the expression as:
\[ \frac{1}{3^{17}} \div \frac{1}{8^{14}} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{1}{3^{17}} \times 8^{14} \]
This can be simplified to:
\[ \frac{8^{14}}{3^{17}} \]
Now, we have transformed the original expression \( 3^{-17}/8^{-14} \) into:
\[ \frac{8^{14}}{3^{17}} \]
with all positive exponents. This is the final expression equivalent to the original with positive exponents only:
\[ \frac{8^{14}}{3^{17}} \]
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