Question

(3x²y³)(-5xy^{4}z)

When multiplying the variables, do you multiply the x by the x next to the y^{4}z, and the y with the y^{4}? I asked my teacher this question for a similar problem and he said not to. When I asked my dad for help with this problem, he said that you do and the answer is -15x^{3}y^{7}z. Which method is correct?

Answer 1

remember
x^m=x times itself m times

REMEMBER THAT MULCTIPLICATION IS COMMUTATIVE
a(bc)=(ab)c


so basically
(abc)(3ac)=a*b*c*3*a*c=a*a*c*c*b*3=3a^2bc^2
group and regroup and move around


so in your problem
(3x^2y^3)(-5xy^4z)=
(3)(x^2)(y^3)(-5)(x)(y^4)(z)=
(3)(-5)(x^2)(x)(y^3)(y^4)(z)=
(-15)(x^3)(y^7)(z)=
-15x^3y^7z