How To Simplify [(1/2)^2-(1/4)^-2, (-3xy^4)-(-4x^3y^6) And (5ab^2/c^3)^2?

1) (1/2)² - (1/4)^-2
  = (2^-1)² - (4^-1)^-2
  = 2^-2 - 4²
  = 1/4 - 16
  = -15 3/4
  = -63/4

2) Change the sign on the second term and you have it. (-1*-4=+4) The terms don't add. You can factor out xy⁴, but "simplify" generally means to multiply it out.

3) (5ab²/c³)² = 25a²b⁴/c⁶