To simplify the expression \((15 - 3 \cdot 47) \cdot 04^{-3}\), we start by calculating \(15 - 3 \cdot 47\).
First, we compute \(3 \cdot 47\): \[ 3 \cdot 47 = 141. \]
Now we substitute this back into the equation: \[ 15 - 141 = -126. \]
Now our expression becomes: \[ -126 \cdot 04^{-3}. \]
Since \(04\) is simply \(4\), we rewrite this as: \[ -126 \cdot 4^{-3}. \]
The next step is to rewrite \(-126\) in a form related to exponents of \(4\): \[ -126 = -1 \cdot 126 = -1 \cdot (4^3 - 11). \]
However, for the purposes of relating it to the exponent properties, we'll focus on: \[ -126 \cdot 4^{-3} = -126 / 4^3. \] Since \(4^3 = 64\), we can simplify: \[ = -126 / 64. \]
At this moment, we see that we need to express this in the context of the responses given. Since there isn't a direct equivalence in terms of a clean exponentiation, let’s analyze each provided response:
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\(60 \cdot 4^{-3}\) – This corresponds to a positive factor of some value times \(4^{-3}\), and while it relates to exponents, it doesn't represent the outcome accurately.
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\(1 \cdot 4^{-3}\) – This simplifies to \(4^{-3}\) which does not reflect the entire expression.
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\(\frac{1}{64}\) – This denotes \(4^{-3}\) but with no negative aspect reflected, which does not match.
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\(64\) – Clearly unrelated.
The only viable option among these that can closely relate to our outcome while reflecting power rules, primarily dealing with how negative influences affect overall stability, demonstrates we can creatively write: \[ -126 = -1 \cdot \frac{126}{64} \cdot 4^3. \]
However, if we were to select one, option 3 \( \frac{1}{64}\) maintains related characteristics, referring back to the inverse of \(4^3\), while option (format not fully achieving this structure) but not transforming into a beneficial relationship across all integers.
Thus, among available choices, none fully encapsulates the total expression we derived through integer exponent states. This indicates a likely need for reevaluation of the base extraction requested initially. The suggestion here being that simplistically none match declared but associatively perhaps, third shows closest through exponent attribution-based relation albeit contextually incomplete.
If you would like further assistance or more exploration into additional fundamental terms, feel free to inquire!