Final answer:
To simplify the expression (2² × 7! ÷ (-64 × 7⁵)), first calculate each component separately, then perform the division. The simplified expression is approximately 0.01875, which is equivalent to (1/53.28).
Step-by-step explanation:
To simplify the expression (2² × 7! ÷ (-64 × 7⁵)), we need to calculate each component separately and then perform the division.
First, let's calculate 2² which equals 4.
Then, let's calculate 7! (7 factorial). This is the product of all positive integers from 1 to 7, which is 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
Next, let's calculate (-64 × 7⁵) which equals -64 × 7 × 7 × 7 × 7 × 7 = -64 × 16807 = -1,073,728.
Now, we can perform the division: (4 × 5040) ÷ -1,073,728 = -20,160 ÷ -1,073,728 = 1/53.28 = 0.01875 (rounded to 5 decimal places).
Therefore, the simplified expression is approximately 0.01875, which is equivalent to (1/53.28).