Simplify and express it in rational form with positive exponents. $(\frac{{(6 x^{3})}^{2} (6 y^{3})}{{(9 x y)}^{6}})$ $(((6x^3)^2(6y^3))/((9xy)^6))$ ?

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Answer 1 · 2018-02-14T02:44:27

The answer is $\frac{8}{19683 y^{3}}$ $8/(19683y^3)$ .

${(x y)}^{a} = x^{a} y^{a}$ $(xy)^a=x^ay^a$

Here's the actual problem:

$\frac{{(6 x^{3})}^{2} (6 y^{3})}{{(9 x y)}^{6}}$ $((6x^3)^2(6y^3))/((9xy)^6)$

$\frac{(6^{2} {(x^{3})}^{2}) (6 y^{3})}{{(9 x y)}^{6}}$ $((6^2(x^3)^2)(6y^3))/((9xy)^6)$

$\frac{(36 x^{6}) (6 y^{3})}{{(9 x y)}^{6}}$ $((36x^6)(6y^3))/((9xy)^6)$

$\frac{216 x^{6} y^{3}}{{(9 x y)}^{6}}$ $(216x^6y^3)/((9xy)^6)$

$\frac{216 x^{6} y^{3}}{9^{6} x^{6} y^{6}}$ $(216x^6y^3)/(9^6x^6y^6)$

$\frac{216 x^{6} y^{3}}{531441 x^{6} y^{6}}$ $(216x^6y^3)/(531441x^6y^6)$

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

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

$8/(19683y^3)$

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

Simplify and express it in rational form with positive exponents. (((6x^3)^2(6y^3))/((9xy)^6))((6x3)2(6y3)(9xy)6)(((6x^3)^2(6y^3))/((9xy)^6))?