Simplify the expression: 6 × [28 ÷ 84 × {36 × 49 ÷ (6 × 7)}].

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Step-by-step solution:

Given expression: 6 × [28 ÷ 84 × {36 × 49 ÷ (6 × 7)}]

1. Calculate the denominator inside the curly braces:
   6 × 7 = 42

2. Calculate the expression inside the curly braces:
   36 × 49 ÷ 42

First, multiply 36 × 49:
   36 × 49 = 1764

Now divide by 42:
   1764 ÷ 42 = 42

3. Now the expression inside the square brackets becomes:
   28 ÷ 84 × 42

4. Calculate 28 ÷ 84:
   28 ÷ 84 = 1/3

5. Multiply by 42:
   (1/3) × 42 = 14

6. Finally multiply by 6:
   6 × 14 = 84

Therefore, the simplified value of the expression is 84.

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