How do you simplify #\frac{3y^{9}}{2y^{4}}\div \frac{9y}{10y^{3}}#?

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Answer 1 · 2016-10-03T02:04:39

#5/3 y^7#

#frac{3y^9}{2y^4}-:frac{9y}{10y^3}#

To divide fractions, multiply by the reciprocal of the second.

#frac{3y^9}{2y^4} * frac{10y^3}{9y}#

#frac{cancel3y^9}{2y^4} * frac{10y^3}{cancel(9)_color(blue)3y}#

#frac{y^9}{cancel2y^4} *frac{cancel(10)^color(blue)5y^3}{3y}#

#frac{y^9}{y^4}*frac{5y^3}[3y}#

Recall the rule #x^a*x^b=x^(a+b)#

#(5y^12)/(3y^5)#

And then use the rule #x^a/x^b=x^(a-b)#

#(5y^7)/3# or #5/3y^7#