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1. If a : b = b : c, then a⁴ : b⁴ is equal to = ?

A. ac : b²

B. a² : c²

C. c² : a²

D. b² : ac

Solution:

\begin{aligned} a : b = b : c \\ \frac{a}{b} = \frac{b}{c} \\ b^{2} = a c \\ b^{4} = a^{2} c^{2} \\ ∴ a^{4} : b^{4} = \frac{a^{4}}{b^{4}} \\ = \frac{a^{4}}{a^{2} c^{2}} \\ = \frac{a^{2}}{c^{2}} \\ = a^{2} : c^{2} \end{aligned}

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