Must two quantities have the same dimensions

[Nikhil faraday]

Must two quantities have the same dimensions if you are using one quantity as an exponent in raising other to a power?
What is the dimension ( or dimensionless) of '2' in mv2/r ?( v is raised to the second power)

 

[scottdave]

The exponent should be dimensionless. The simple answer is: v² means v times v.

 

[Dale]

Must two quantities have the same dimensions if you are using one quantity as an exponent in raising other to a power?

To second what @scottdave said, the exponent must be dimensionless. Also the argument to a sin or cos or other trig function or a log must all be dimensionless.

 

[scottdave]

I admit that it is difficult to think of what (velocity)² could mean. (Length)² is easy enough to understand that is Area. (length)³is volume.
Even Acceleration (meters / sec²) might at first seem baffling, but you can rewrite it as (meters per second) per second.

Think of it like this: 9.8 meters per second per second. What does it mean? Every second, a falling object gains another 9.8 m/s of velocity.