@Manmay..on dividing both sides by bα
This can be written as \left((\frac{a}{b})^{\alpha } + 1 ) \right)^{\frac{1}{\alpha }} = (p^{x} + 1)^{\frac{1}{x }}
where p is a constant = a/b
Now see the Functions..whether it's increasing or decreasing...
looking at the question it seems the function is decreasing for x > 0