Final answer:
The value of the expression 8! / ((4!)² ✕ (4!)²) is 0.1216
Step-by-step explanation:
To find the value of the expression 8! / ((4!)² ✕ (4!)²), we need to first calculate the value of each factorial. The notation 8! represents the product of all positive integers up to 8, so 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. Similarly, 4! is calculated as 4 × 3 × 2 × 1.
Now, let's substitute the values back into the expression. (4!)² is equal to (4 × 3 × 2 × 1)² = 24². Therefore, the expression becomes 8! / (24² ✕ 24²).
To calculate the value of 8!, we multiply all the numbers from 1 to 8, which gives us 40320. Substituting this value back into the expression, we get 40320 / (24² ✕ 24²).
Next, let's calculate (24² ✕ 24²). This expression is equal to 576 × 576 = 331776. Therefore, the expression simplifies to 40320 / 331776.
Dividing these two numbers, we get the final value of the expression: 0.1216.