We will multiply each common term in parenthesis with the common term in the other parenthesis:
(color(red)(3)color(blue)(x^2)color(green)(y))(color(red)(10)color(blue)(x^5)color(green)(y^3)) -> (color(red)(3) xx color(red)(10))(color(blue)(x^2) xx color(blue)(x^5))(color(green)(y) xx color(green)(y^3))(3x2y)(10x5y3)→(3×10)(x2×x5)(y×y3)
We can multiply the constants and use the rules for exponents to multiply the common terms.
x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a)+color(blue)(b)xa×xb=xa+b
and
z = z^(color(red)(1)z=z1
This gives:
(color(red)(3) xx color(red)(10))(color(blue)(x^2) xx color(blue)(x^5))(color(green)(y) xx color(green)(y^3)) =(3×10)(x2×x5)(y×y3)=
color(red)(30)color(blue)(x^(2+5))color(green)(y^(1+3)) = 30x2+5y1+3=
color(red)(30)color(blue)(x^7)color(green)(y^4)30x7y4
