Reduce to lowest terms 4x^3y^4/-8xy^2

= (4x^3y^4)/(-8xy^2)
simplify exponents by subtracting the denominator exponent from numerator exponent [x^(3-1)]

= (4x^3y^4)/(-8xy^2)
simplify -4/8 by 4 into numerator and denominator

= (-1x^2y^2)/2

= (-x^2y^2)/2

ANSWER: (-x^2y^2)/2

Hope this helps! :)