To simplify the expression \((15 - 3 \cdot 4^7)^0 / 4^{-3}\), let's start by breaking it down step by step.
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Evaluate \( (15 - 3 \cdot 4^7)^0 \):
- Any non-zero number raised to the power of 0 is equal to 1. Therefore, \( (15 - 3 \cdot 4^7)^0 = 1 \).
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Now, we have: \[ 1 / 4^{-3} \]
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Simplifying \( 1 / 4^{-3} \):
- Using the property of exponents that states \( a^{-n} = \frac{1}{a^n} \), we have: \[ 1 / 4^{-3} = 4^{3} \]
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Calculating \( 4^{3} \):
- \( 4^3 = 64 \).
Through these steps, we find that: \[ \frac{(15 - 3 \cdot 4^7)^0}{4^{-3}} = 64 \]
Therefore, the equivalent expression is 64.