If a : b = b : c, then a⁴ : b⁴ is equal to = ?
a) ac : b²
b) a² : c²
c) c² : a²
d) b² : ac

Answer: b
Explanation:
$$\eqalign{ & a:b = b:c \cr & \frac{a}{b} = \frac{b}{c} \cr & {b^2} = ac \cr & {b^4} = {a^2}{c^2} \cr & {a^4}:{b^4} = \frac{{{a^4}}}{{{b^4}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^4}}}{{{a^2}{c^2}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^2}}}{{{c^2}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {a^2}:{c^2} \cr} $$