( 1 ) ( n^n )^n^n = n^n^n+1 .. OR : ( a^b )^b^c = a^b^c+1 .. where : ( c+1 ) is the power of ( b ).

( 2 ) ( n^n^n )^n^n = n^n^2n .. OR : ( a^b^c )^b^e = a^b^c+1 .. where : ( c+1 ) is the power of ( b ).

( 3 ) ( n^n^n^n )^n = n^n^d : where : d = ( n^n )+1 .. OR : ( a^b^c^d )^b = a^b^f : where : f = (c^d )+1.

( 4 ) ( n^n^n^n )^n^n = n^n^h : where : h = ( n^n )+n .. OR : ( a^b^c^d )^b^e = a^b^g : where : g = ( c^d )+e .

( 5 ) ( n^n )^n^n^n = n^n^c : where : c = ( n^n )+1 ..

( 6 ) ( n^n^n )^n^n^n = n^n^f : where : f = ( n^n )+n .. OR : ( a^b^c )^b^a^c = a^b^g : g = ( a^c )+c ..

( 7 ) ( n^n^n^n )^n^n^n = n^n^h : where : h = 2( n^n ) ..

( 8 ) ( n^n^n^n )^n^n^n^n = n^n^d : where : d = ( n^n^n ) + ( n^n ) ..

All the last digits are the nature numbers .

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