Can you factorial a power?

Question

I know this may be a straight forward question, but I looked around on google for about 20 minutes to find nothing. I am currently a year 8 student and came across a problem where I have to find the highest number using the four following numbers: $9, 5, -8$ and $-2$. I could use any mathematical I wanted to use, so I just used factorials. I came up with $(9! \times 5!)\times(-8x-2)!$, then, I came up with $5!^{9!}$ and then $9!^{(-8 \times-2)!}$. It may come up in a test and I didn't demonstrate this in class. Does this equation work and is there a higher number I could get with mathematical notation I don't know about? (Note - I can't use infinity.) Thanks.

Answer 1

yes you can include factorial in the exponent. but simpler would be $9!!!!!!! $ or $9^9^9^9^9^9^9$ or even further forms to make numbers bigger see https://en.m.wikipedia.org/wiki/Knuth%27s_up-arrow_notation