Answer:
[tex]-\frac{x^2y^2}{2}[/tex]
Step-by-step explanation:
We have an extremely large equation and are asked to divide it, so let's solve it step-by-step :
Remove the parenthesis to make it easier to read :
[tex]\frac{-3x^3 *2x^3y^4z *3z^2}{4x^3z*3yz*3xyz}[/tex]
Multiply the numerators :
[tex]\frac{-18x^6y^4z^3}{4*3*3x^3yyzzz}[/tex]
Multiply the denominators :
[tex]\frac{-18x^6y^4z^3}{36x^4y^2z^3}[/tex]
Apply the negative rule :
[tex]-\frac{18x^6y^4z^3}{36x^4y^2z^3}[/tex]
Cancel the common factor which is 18 :
[tex]-\frac{x^6y^4z^3}{2x^4y^2z^3}[/tex]
Apply the addition exponent rule :
[tex]\frac{y^4z^3x^{6-4} }{2y^2z^3}[/tex]
Subtract :
[tex]\frac{x^2y^4z^3 }{2y^2z^3}[/tex]
Apply the rule for y :
[tex]\frac{x^2y^{4-2} z^3 }{2z^3}[/tex]
Subtract :
[tex]\frac{x^2y^2z^3 }{2z^3}[/tex]
Cancel the common factor of z^3 :
[tex]-\frac{x^2y^2}{2}[/tex]
