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))#

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)#

and

#z = z^(color(red)(1)#

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)) =#

#color(red)(30)color(blue)(x^(2+5))color(green)(y^(1+3)) = #

#color(red)(30)color(blue)(x^7)color(green)(y^4)#