Finding the power and constant from two pairs of values

The quantity \(y\) is directly proportional to \(x^n\), where \(n\) is a constant and \(x>0\).

1. Show that for any two pairs \((x_1,y_1)\) and \((x_2,y_2)\) of corresponding values, \(\dfrac{y_2}{y_1}=\left(\dfrac{x_2}{x_1}\right)^n\).[2]
2. When \(x=3\), \(y=12\), and when \(x=6\), \(y=96\). Find \(n\) and the constant of proportionality.[3]
3. Hence find the value of \(x\) for which \(y=1500\).[2]