To simplify the expression \( \frac{4^0 \cdot 5^{-2}}{(-2)^{-3}} \) using the properties of integer exponents, we will first evaluate each term one by one.
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Evaluate \( 4^0 \): \[ 4^0 = 1 \]
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Rewrite \( 5^{-2} \): \[ 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \]
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Rewrite \( (-2)^{-3} \): \[ (-2)^{-3} = \frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8} \]
Now substitute these back into the expression:
\[ \frac{4^0 \cdot 5^{-2}}{(-2)^{-3}} = \frac{1 \cdot \frac{1}{25}}{-\frac{1}{8}} \]
This simplifies to:
\[ \frac{\frac{1}{25}}{-\frac{1}{8}} = \frac{1}{25} \cdot -8 = -\frac{8}{25} \]
Therefore, the equivalent expression simplified with only positive exponents is:
\[ -\frac{8}{25} \]
Thus, the final answer is:
\[ \boxed{-\frac{8}{25}} \]