How do you simplify #(x^3y^4)/( x^9y^2)# using only positive exponents?

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Answer 1 · 2016-06-30T16:10:54

#y^2/x^6#

If we expand #(x^3y^4)/(x^9y^2)#

We see that the number of variables in the fraction become

#(x*x*x*y*y*y*y)/(x*x*x*x*x*x*x*x*x*y*y)#

We can now cancel the similar variables

#(cancel(x*x*x)*cancel(y*y)*y*y)/(cancel(x*x*x)*x*x*x*x*x*x*cancel(y*y))#

We are left with

#(y*y)/(x*x*x*x*x*x)#

Which becomes

#y^2/x^6#

Or by using the properties of exponents

We can change #(x^3y^4)/(x^9y^2)# to

#x^3x^-9y^4y^-2#

Which becomes

#x^(3-9)y^(4-2)#

Which becomes
#x^-6y2#

Eliminating the negative exponent by placing it in the denominator we get

#y^2/x^6#