If a : b = b : c, then a⁴ : b⁴ would be equal to

$$\eqalign{ & = \frac{a}{b} = \frac{b}{c} \cr & \Rightarrow {b^2} = ac \cr & \Rightarrow \frac{{{a^4}}}{{{b^4}}} = \frac{{{a^4}}}{{{{\left( {ac} \right)}^2}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^4}}}{{{a^2}{c^2}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^2}}}{{{c^2}}} \cr & \Rightarrow {a^4}:{b^4} = {a^2}:{c^2} \cr} $$