5756(8:8)(7678+66)

To solve the expression \( 5756(8:8)(7678 + 66) \), let's break it down step by step:

1. Calculate \( 8:8 \): \[ 8:8 = \frac{8}{8} = 1 \]

2. Calculate \( 7678 + 66 \): \[ 7678 + 66 = 7744 \]

3. Now substitute these back into the original expression: \[ 5756(1)(7744) \]

4. This simplifies to: \[ 5756 \times 7744 \]

5. Now, we perform the multiplication: \[ 5756 \times 7744 = 44560224 \]

Thus, the final result of the expression \( 5756(8:8)(7678 + 66) \) is \( \boxed{44560224} \).