(14a'2:27x'3)'2 * (9x'2:7a'2)'3

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To simplify this expression, we need to first simplify each term raised to a power separately and then multiply them together:

(14a'2:27x'3)'2 = (14^2)(a'2^2)(27^2)(x'3^2)
= 196a^4 * 729x^6

(9x'2:7a'2)'3 = (9^3)(x'2^3)(7^3)(a'2^3)
= 729x^6 * 343a^6

Now, multiply the two simplified expressions together:

(196a^4 729x^6) (729x^6 343a^6)
= 142884a^4 531441x^12 * 343a^6
= 48977651264a^10x^12

So, the simplified expression is 48977651264a^10x^12.