The variable x varies directly as the square of y, and y varies directly as the cube of z. If x equals -16 when z equals 2, what is the value of x when z equals 1/2?
x = k y^2 and y = kz^3 where k = some constant
we can combine the constants and sub z^3 in for y
x = k (z^3)^2 = k z^6 now sub in x = -16 and z = 2
-16 = k (2)^6
k = -1/4
so the equation becomes x = -1/4 z^6 NOW, sub in z = 1/2
x = -1/4 (1/2)^6 = - 1/256