Question

Simplify (6^5/7^3)^2

Answer 1

Simplify the following:
(6^5/7^3)^2

7^3 = 7×7^2:
(6^5/(7×7^2))^2

7^2 = 49:
(6^5/(7×49))^2

7×49 = 343:
(6^5/343)^2

6^5 = 6×6^4 = 6 (6^2)^2:
((6 (6^2)^2)/343)^2

6^2 = 36:
((6×36^2)/343)^2

 | | 3 | 6
× | | 3 | 6
 | 2 | 1 | 6
1 | 0 | 8 | 0
1 | 2 | 9 | 6:
((6×1296)/343)^2

6×1296 = 7776:
(7776/343)^2

(7776/343)^2 = 7776^2/343^2:
7776^2/343^2

 | | | | 7 | 7 | 7 | 6
× | | | | 7 | 7 | 7 | 6
 | | | 4 | 6 | 6 | 5 | 6
 | | 5 | 4 | 4 | 3 | 2 | 0
 | 5 | 4 | 4 | 3 | 2 | 0 | 0
5 | 4 | 4 | 3 | 2 | 0 | 0 | 0
6 | 0 | 4 | 6 | 6 | 1 | 7 | 6:
60466176/343^2

 | | | 3 | 4 | 3
× | | | 3 | 4 | 3
 | | 1 | 0 | 2 | 9
 | 1 | 3 | 7 | 2 | 0
1 | 0 | 2 | 9 | 0 | 0
1 | 1 | 7 | 6 | 4 | 9:

Answer: 60466176/117649