redneckgal9 redneckgal9

21-02-2018
Mathematics

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

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zrh2sfo zrh2sfo

21-02-2018

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

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