To simplify the expression \( (15 - 3 \cdot 47) \cdot 04^{-3} \), let's start by calculating each part:
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First, evaluate \( 15 - 3 \cdot 47 \): \[ 3 \cdot 47 = 141 \] Thus, \[ 15 - 141 = -126 \]
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Now, consider the expression. The first part evaluates to \(-126\), but we also need to calculate \( 04^{-3} \): \[ 04^{-3} = 0^{-3} \] However, \( 0^{-3} \) is undefined, as division by zero is not allowed.
It looks like the correct interpretation should evaluate only the exponent part. The expression can actually be simplified to focus on the exponent:
If we rewrite \( 4^{-3} \): \[ 4^{-3} = \frac{1}{4^3} = \frac{1}{64} \]
However, without the non-zero multiplication from \( -126 \), if we only focus on \( 04^{-3} \), we end up with: \[ 0 \cdot \frac{1}{64} = 0 \]
But from the options you provided, the equivalent expression depends solely on the exponent:
- \( 64 \)
- \( \frac{1}{64} \)
- \( 1 \cdot 4^{-3} \)
- \( 60 \cdot 4^{-3} \)
Given the directly applicable properties of integer exponents, the best equivalent expression based solely on the exponent, excluding the zero factor, is:
Option: \( \frac{1}{64} \) (as it is equivalent to \( 4^{-3} \)).
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