(25!) = 15511210043330985984000000 => (6 zeros)
Detecting Pattern:
(25!) ^ 1 => (15511210…85984000000) => 6 zeros
(25!) ^ 2 => (24059763…48256000000000000) => 12 zeros
(25!) ^ 3 => (37319604…43904000000000000000000) => 18 zeros
(25!) ^ 4 => (57887222…41536000000000000000000000000) => 24 zeros
(25!) ^ 5 => (89790087…31424000000000000000000000000000000) => 30 zeros
and so on..
thus:
Leading Zeros in [ (25!) ^ (25!) ] = [Number of leading zeros in (25!)] * (25!)
[Number of leading zeros in (25!)] = 6 zeros
value of (25!) = 15511210043330985984000000
leading zeros in (25!)^(25!) = 6 * 15511210043330985984000000
= 93067260259985915904000000 zeros