5 to_power 5 =
5 to_power (4 + 1)
.=
(5 to_power 4) * (5 to_power 1)
by POWER:27
.=
(5 to_power (3 + 1)) * 5
by POWER:25
.=
((5 to_power 3) * (5 to_power 1)) * 5
by POWER:27
.=
((5 to_power (2 + 1)) * 5) * 5
by POWER:25
.=
(((5 to_power 2) * (5 to_power 1)) * 5) * 5
by POWER:27
.=
(((5 to_power (1 + 1)) * 5) * 5) * 5
by POWER:25
.=
((((5 to_power 1) * (5 to_power 1)) * 5) * 5) * 5
by POWER:27
.=
((((5 to_power 1) * 5) * 5) * 5) * 5
by POWER:25
.=
(((5 * 5) * 5) * 5) * 5
by POWER:25
.=
3125
;
hence
5 to_power 5 = 3125
; verum