Question

Choose the correct simplification of the expression (3x^2y^3z^4)(2x^5y^2z^3)

I'm so confused if someone could help with the simplification,

Answer 1

6x^(2+5) y^(3+2) z^(4+3) =
6x^7 y^5 z^7

Answer 2

Answer: hello there!

we have the expression
`(3x^2y^3z^4)(2x^5y^2z^3)` and we want to simplify it.

A useful equality is:

`x^(a)x^(b) =x^(a+b)`

then the first thing we need to do is group the therms alike:

`(3x^2y^3z^4)(2x^5y^2z^3) = (3*2)(x^(2) *x^(5))(y^(3)*  y^(2))*(z^(3)  *z^(4))`

`= 6x^(2+5)y^(3+2)z^(4+3)  =6x^(7)y^(5) z^(7)`

now we can simplify it a bit more using:

`x^(a) y^(a)=(xy)^(a)`

`6x^(7)y^(5) z^(7)= 6(xzy)^(7) y^(-2) =6((xyz)^(7) )/(y^(2) )`