𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Evaluate (8!-6(6!))/(3!+4)

𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:

First, let's evaluate the numerator:

8! - 6(6!)

Recall that 8! = 8 × 7 × 6! = 56 × 6!

So, the numerator becomes:

56 × 6! - 6 × 6!

Factor out 6!:

(56 - 6) × 6! = 50 × 6!

Now, let's evaluate the denominator:

3! + 4

Recall that 3! = 3 × 2 × 1 = 6

So, the denominator becomes:

6 + 4 = 10

Now, divide the numerator by the denominator:

(50 × 6!) / 10

= 5 × 6!

To get a numerical value, calculate 6!:

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

So, the final value is:

5 × 720 = 3600

Therefore, (8! - 6(6!)) / (3! + 4) = 3600.