(12a-12b)^5/(6a-6b)^5

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To simplify this expression, we can first factor out a common factor of 6 from both terms in the numerator and denominator:

(12a - 12b)^5 / (6a - 6b)^5
= (6(2a - 2b))^5 / (6(a - b))^5
= 6^5 (2a - 2b)^5 / 6^5 (a - b)^5
= (2a - 2b)^5 / (a - b)^5

Now, we can expand the numerator using the binomial theorem:

(2a - 2b)^5 = (C(5,0)(2a)^5(-2b)^0) + (C(5,1)(2a)^4(-2b)^1) + ... + (C(5,5)(2a)^0(-2b)^5)
= (2^5a^5) - (2^45a^42b) + (2^310a^3(2b)^2) - (2^210a^2(2b)^3) + (25a(2b)^4) - (2^0b^5)
= 32a^5 - 160a^4b + 320a^3b^2 - 320a^2b^3 + 160ab^4 - b^5

And expand the denominator in a similar manner:

(a - b)^5 = (C(5,0)a^5(-b)^0) + (C(5,1)a^4(-b)^1) + ... + (C(5,5)a^0(-b)^5)
= a^5 - 5a^4b + 10a^3b^2 - 10a^2b^3 + 5ab^4 - b^5

Therefore, the simplified expression is:

(32a^5 - 160a^4b + 320a^3b^2 - 320a^2b^3 + 160ab^4 - b^5) / (a^5 - 5a^4b + 10a^3b^2 - 10a^2b^3 + 5ab^4 - b^5)