In accord to principle of homogenity, we cant add/subtract physical quantities which have different dimensions.What is the meaning of dimenson?

Is it power to which a physical quantity is raised.

Pls give a example where physical quantiities of same dimension are added.

“Physical equations must be dimensionally homogeneous.” This is known as the principle of homogeneity of dimensions and according to this principle.

When a physical equation consists of a number of terms, each of these terms must be of the same dimensions in each of the fundamental units.

One can state the principle in a much simpler way as follows: The powers of mass, length and time in each term on one side of a dimensional equation must always be equal to their respective powers in each term on the other side of the dimensional equation.

According to the principle of homogeneity, the dimensions of each term on the LHS must be equal to the dimensions of the term on the RHS.