How do you divide #\frac { 9x ^ { 6} y } { 27x ^ { 2} y ^ { 5} } \div \frac { x } { 6y ^ { 2} }#?

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Answer 1 · 2016-12-13T20:08:06

#(2x^3)/y^2# or #2x^3y^-2#

We can rewrite this problem as:

#((9x^6y)/(27x^2y^5))/(x/(6y^2))#

The rule for dividing fractions is:

#color(red)((a/b)/(c/d) = (a*d)/(b*c))#

Using this rule we can rewrite our problem as:

#((9x^6y) * (6y^2))/((27x^2y^5)*(x))#

Multiplying the numerator and denominator gives:

#(54x^6y^(1+2))/(27x^(2+1)y^5)#

#(54x^6y^3)/(27x^3y^5)#

Factoring gives:
#(54/27)(x^3/x^3)(y^3/y^3)(x^3/y^2)#

#2 xx 1 xx 1 xx (x^3/y^2)#

#(2x^3)/y^2#