How do you simplify #((6x^2)^2)/(xy^3)*(4x^2y)^2/( xy^2)#?

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Answer 1 · 2015-08-02T14:58:01

#color(red)(((6x^2)^2)/(xy^3)·((4x^2y)^2)/(xy^2) =(576x^6)/y^3)#

You must apply the outside exponent to everything inside the parentheses.

Remember that #(x^m)^n=x^(mn)#.

#((6x^2)^2)/(xy^3)·((4x^2y)^2)/(xy^2) = (36x^4)/(xy^3) · (16x^4y^2)/(xy^2)#

We can immediately cancel the #y^2# term.

#(36x^4)/(xy^3)·(16x^4color(red)(cancel(color(black)(y^2))))/(xcolor(red)(cancel(color(black)(y^2)))) = (36x^4)/(xy^3) · (16x^4)/x#

Now we multiply the two fractions.

Remember that #x^mx^n = x^(m+n)#

#(36x^4)/(xy^3) · (16x^4)/x = (576x^8)/(x^2y^3)#

And now we do our divisions.

Remember that #x^m/x^n = x^(m-n)#

#(576x^8)/(x^2y^3) = (576x^6)/y^3#

∴ #((6x^2)^2)/(xy^3)·((4x^2y)^2)/(xy^2) =(576x^6)/y^3#