Question

(7!)^2 - (3!)^2 / (9!)^2

Answer 1

(7!)^2 - (3!)^2 / (9!)^2=25401600-(36/131681894400)=25401600

Answer 2

To calculate the expression (7!)^2 - (3!)^2 / (9!)^2, let's break it down step by step.

First, we need to evaluate the factorials. The factorial of a number is the product of all positive integers less than or equal to that number.

(7!) = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

(3!) = 3 x 2 x 1 = 6

(9!) = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ≈ 3.63 x 10^6

Now, let's substitute these values back into the expression:

(7!)^2 - (3!)^2 / (9!)^2 = (5040)^2 - (6)^2 / (3.63 x 10^6)^2

Calculating the squares:

(5040)^2 = 25,401,600

(6)^2 = 36

(3.63 x 10^6)^2 = 13.1769 x 10^12

Now, substituting the values into the expression:

25,401,600 - 36 / 13.1769 x 10^12

Performing the division:

25,401,600 - 36 ÷ 13.1769 x 10^12

Finally, calculating the expression:

25,401,600 - 36 ÷ 13.1769 x 10^12 ≈ 25,401,600 - 2.73 x 10^-12 ≈ 25,401,600.