Question

how can we show that liquid exerts pressure which varies with depth​

Answer 1

Take a water bottle with three holes in it. The holes must be on the top,the bottom and in the middle. Pour water into it. Water falls the farthest from the lower hole and water from the upper hole falls near the bottle. The water from the hole in the middle is placed between the former two. Thus we can understand that pressure increases when we go deeper

Answer 2

The pressure exerted by liquid increases with increasing depth inside the liquid. But as we go deeper in a liquid the pressure of liquid increases. As the depth of liquid increases the weight of liquid column pushing down from above increases and hence the pressure also increases.