Question

Evaluate.



(14)−2−(50⋅2)⋅1−1



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Answer 1

Let's simplify the expression step by step:

1. Start with the given expression:
\[
14^{-2} - (50 \cdot 2) \cdot 1 - 1
\]

2. Calculate \(14^{-2}\):
\[
14^{-2} = \frac{1}{14^2} = \frac{1}{196}
\]

3. Calculate \(50 \cdot 2\):
\[
50 \cdot 2 = 100
\]

4. Now substitute back into the expression:
\[
\frac{1}{196} - 100 \cdot 1 - 1
\]
Simplifies to:
\[
\frac{1}{196} - 100 - 1
\]

5. Combine \(100\) and \(1\):
\[
100 + 1 = 101
\]

6. The expression now is:
\[
\frac{1}{196} - 101
\]

7. To perform the subtraction, convert \(101\) to a fraction with a denominator of 196:
\[
101 = \frac{101 \cdot 196}{196} = \frac{19896}{196}
\]

8. 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 \( \boxed{\frac{-19895}{196}} \).