Answer: hello there!
we have the expression [tex](3x^2y^3z^4)(2x^5y^2z^3)[/tex] and we want to simplify it.
A useful equality is:
[tex]x^{a}x^{b} =x^{a+b}[/tex]
then the first thing we need to do is group the therms alike:
[tex](3x^2y^3z^4)(2x^5y^2z^3) = (3*2)(x^{2} *x^{5})(y^{3}* y^{2})*(z^{3} *z^{4})[/tex]
[tex]= 6x^{2+5}y^{3+2}z^{4+3} =6x^{7}y^{5} z^{7} [/tex]
now we can simplify it a bit more using:
[tex]x^{a} y^{a}=(xy)^{a}[/tex]
[tex]6x^{7}y^{5} z^{7}= 6(xzy)^{7} y^{-2} =6\frac{(xyz)^{7} }{y^{2} }[/tex]
