Let's break down the expression step by step:
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Calculate \((-2025)^0\): Any non-zero number raised to the power of 0 is 1. \[ (-2025)^0 = 1 \]
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Calculate \(-4^{-2}\): \[ -4^{-2} = -\frac{1}{4^2} = -\frac{1}{16} \]
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Calculate \(2^{-3}\): \[ 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \]
Now substituting these values back into the expression:
\[ 3(-2025)^0 - 4^{-2} + 2^{-3} = 3(1) - \left(-\frac{1}{16}\right) + \frac{1}{8} \]
This simplifies to:
\[ 3 + \frac{1}{16} + \frac{1}{8} \]
To add these fractions, we need a common denominator. The smallest common denominator for 16 and 8 is 16.
Convert \(\frac{1}{8}\) to have a denominator of 16:
\[ \frac{1}{8} = \frac{2}{16} \]
Now, we can add the fractions:
\[ 3 + \frac{1}{16} + \frac{2}{16} = 3 + \frac{3}{16} \]
Expressing \(3\) as a fraction with the same denominator:
\[ 3 = \frac{48}{16} \]
Now adding everything:
\[ \frac{48}{16} + \frac{3}{16} = \frac{51}{16} \]
Thus, the final answer is:
\[ \frac{51}{16} \]
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