How do you simplify #(2x^4y^-4z^-3)/(3x^2y^-3z^4)# and write it using only positive exponents?

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Answer 1 · 2017-01-28T10:10:52

#(2x^2)/(3yz^7)#

We start with:

#(2x^4y^-4z^-3)/(3x^2y^-3z^4)#

I'm first going to rewrite this using the rule #x^-1=1/x#:

#2/3 x^4y^-4z^-3x^-2y^3z^-4#

and rearrange terms and group like terms:

#2/3 (x^4x^-2)(y^-4y^3)(z^-3z^-4)#

We can now use the rule #x^a xx x^b=x^(a+b)#

#2/3 (x^(4-2))(y^(-4+3))(z^(-3-4))#

#2/3 x^2y^-1z^-7#

and now let's write this using only positive exponents:

#(2x^2)/(3yz^7)#