Let's simplify the expression step by step:
-
Start with the given expression:
\[ 14^{-2} - (50 \cdot 2) \cdot 1 - 1 \] -
Calculate \(14^{-2}\):
\[ 14^{-2} = \frac{1}{14^2} = \frac{1}{196} \] -
Calculate \(50 \cdot 2\):
\[ 50 \cdot 2 = 100 \] -
Now substitute back into the expression:
\[ \frac{1}{196} - 100 \cdot 1 - 1 \] Simplifies to: \[ \frac{1}{196} - 100 - 1 \] -
Combine \(100\) and \(1\):
\[ 100 + 1 = 101 \] -
The expression now is:
\[ \frac{1}{196} - 101 \] -
To perform the subtraction, convert \(101\) to a fraction with a denominator of 196:
\[ 101 = \frac{101 \cdot 196}{196} = \frac{19896}{196} \] -
Now subtract the two fractions:
\[ \frac{1}{196} - \frac{19896}{196} = \frac{1 - 19896}{196} = \frac{-19895}{196} \]
Thus, the final answer is:
\[
\frac{-19895}{196}
\]
In decimal form, this is approximately \(-101.0051\). The exact value in fraction form is \( \boxed{\frac{-19895}{196}} \).
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