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

1 Answer
Jun 30, 2016

Answer:

#y^2/x^6#

Explanation:

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#