Simplify and express it in rational form with positive exponents. #(((6x^3)^2(6y^3))/((9xy)^6))#?

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Answer 1 · 2018-02-14T02:44:27

The answer is #8/(19683y^3)#.

#(xy)^a=x^ay^a#

Here's the actual problem:

#((6x^3)^2(6y^3))/((9xy)^6)#

#((6^2(x^3)^2)(6y^3))/((9xy)^6)#

#((36x^6)(6y^3))/((9xy)^6)#

#(216x^6y^3)/((9xy)^6)#

#(216x^6y^3)/(9^6x^6y^6)#

#(216x^6y^3)/(531441x^6y^6)#

#(8color(red)(cancel(color(black)(x^6)))y^3)/(19683color(red)(cancel(color(black)(x^6)))y^6)#

#(8color(red)(cancel(color(black)(y^3))))/(531441y^(color(red)(cancel(color(black)(6)))3))#

#8/(19683y^3)#

Unfortunately, this big fraction can't be simplified any further.