Cyclicity and exponents

If you are a smart guy, look quickly: The unit of 58 is 8. And the power of 8 has the unit are even numbers: 2, 4, 6, 8.

58 is an even number if we multiply several times also we can get only an even number

$For\quad this\quad question\quad cyclicity\quad of\quad 8\quad can\quad be\quad calculated\quad by\quad it\quad square\quad root\quad chart\\ { 8 }^{ 1 }\quad =\quad 8\\ { 8 }^{ 2 }\quad =\quad 64\\ { 8 }^{ 3 }\quad =\quad 512\\ { 8 }^{ 4 }\quad =\quad 4,096\\ { 8 }^{ 5 }\quad =\quad 32,768\\ { 8 }^{ 6 }\quad =\quad 2,62,144\\$ And note we only need to see the units place