(3y^2 /(10x^2) )(5x/(2y))

= (3*5)/(10*2)*y^2*x^-2*x*y^-1

= (3/4)*y^(2-1)*x^(-2+1)

= (3/4)*y^1*x^-1

= (3y)/(4x)

As you have written the expression--without parentheses around denominator terms--the interpretation must be

(3y^2/10)x^2*(5x/2)y

= (3x^3*y^3)/4

= (3*5)/(10*2)*y^2*x^-2*x*y^-1

= (3/4)*y^(2-1)*x^(-2+1)

= (3/4)*y^1*x^-1

= (3y)/(4x)

As you have written the expression--without parentheses around denominator terms--the interpretation must be

(3y^2/10)x^2*(5x/2)y

= (3x^3*y^3)/4