Question : If a : b = b : c, then what is the value of a6 : b6?
Option 1: a3 : b3
Option 2: b3 : ac
Option 3: a3 : c3
Option 4: a2 : b2
Correct Answer: a 3 : c 3
Solution :
a : b = b : c
$⇒\frac{\text{a}}{\text{b}} = \frac{\text{b}}{\text{c}}$
$⇒ \text{b}^2 = \text{ac}$
Cubing on both sides, we get,
$⇒ \text{b}^6 = \text{a}^3\text{c}^3$
$⇒ \frac{\text{a}^6}{\text{b}^6} = \frac{\text{a}^6}{\text{a}^3 \text{c}^3}$
$⇒ \frac{\text{a}^6}{\text{b}^6} = \frac{\text{a}^3}{\text{c}^3}$
Hence, the correct answer is $\text{a}^3: \text{c}^3$.
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