To simplify the expression \( 4(0) \cdot 5^{-2} \cdot (-2) \cdot (-3) \) using properties of exponents and ensuring we only have positive exponents, we first need to interpret the expression.
It's important to clarify that \( 4(0) \) implies \( 4 \cdot 0 \), which equals \( 0 \). Therefore, any multiplication involving \( 0 \) yields \( 0 \).
However, let's consider ignoring the term \( 4(0) \) and focus instead on simplifying \( 5^{-2} \cdot (-2) \cdot (-3) \).
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Rewrite \( 5^{-2} \): \[ 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \]
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The remaining expression is: \[ (-2) \cdot (-3) = 6 \]
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Now we combine the fractions: \[ \frac{1}{25} \cdot 6 = \frac{6}{25} \]
Thus, while the term \( 4(0) \) would contribute \( 0 \) to the entire expression, if we strictly focus on the calculations provided, the final simplified expression from the other terms is:
\[ \frac{6}{25} \]
However, because \( 4(0) \) leads to \( 0 \), the overall result when combining would yield \( 0 \).
Final answer considering the terms collectively: \[ \text{Overall Result: } 0 \] Otherwise, the equivalent expression without \( 4(0) \) simplifies to: \[ \frac{6}{25} \]