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 $x^m/x^n = x^(m-n)$

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

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

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