combining the index and columns/rows function

Hi - I have the following function which increments across columns as if going down through rows of one column:

=SUM(POWER(INDEX($AC:$AC,COLUMNS($AC$1:AC1)),$Z$1)) - call this row 1, column 1

I am happy with this and now have one row with the correct data. However now I wish to do increment this working method to next row etc so that I get:

=SUM(POWER(INDEX($AC:$AC,COLUMNS($AC$1:AC1)),$Z$2)) - call this row 2, column 1

just by dragging cell 1 down.

Does anyone have any idea of how this is done?

When I do this at the moment I get the same result from the first cell. I don't want to take the dollar signs away from Z as I want to stick to Z1 for row one as I increment through columns A to Z for example.

Thanks.

I guess to sum up I want $Z$ when dragging across, but want Z when dragging down. An impossible situation I know, but racking my brains to find a work around. I have a lot of data so can't afford to be doing it by hand.

Thanks! I'm clearly showing how much of a novice I am. Works like a charm.