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Answer 1

Question a:

`((2^3)^6 * 9^3)/(4^2 * 27)\\= (2^(18) * 3^6)/(2^4 * 3^3)\\=2^(14) * 3^3`

Question b:

`(35 * 7^3)/(5^2 * 343)\\= (7 * 5^1 * 7^3)/(5^2 * 7^3)\\= (5^1 * 7^4)/(5^2 * 7^3)\\=(7^1)/(5^1) = (7)/(5)`

Question c:

Note that this one is particularily simple as anything to the power of zero is equal to 1

`(((2^4 * 3^6)/(12^2))^0)^3\\= 1^3\\ =1`

Question d:

`(13^3 * 7^0)/(((65 * 49)^2)^1)\\(13^3)/((65 * 49)^2)\\(13^3)/((13 * 5 * 49)^2)\\(13^3)/(13^2 * 5^2 * 7^4)\\(13)/(5^2 * 7^4)`