Simplify. Assume that no denominator is zero. (3y^2 /10x^2 ) X (5x/2y)?

(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