What is the easiest way to make multiple equally spaced circles that share the same center point?

I'd say using the interpolate subpaths live path effect although technically that creates a compound path.

For circle objects try tiled cloning. Although that has limitation on the exact size, can work with percentage values only for the growth.

How do I get tiled clones to enlarge exponentially from the original and share the same center point instead of creating new rows and columns?

After testing it seems the shifting settings cannot be set perfect for the purpose.

Let's say you want to draw 24 concentric circles,
then with the tiled clones set 24 rows, 1 columns, set -100% for y shifting per row, and
scale x and scale y to 50% per row and create.

After that, select the clones and use the align and distribute panel (Shift+Ctrl+A) to align the clones on a horizontal axis.

Lazur wrote:I'd say using the interpolate subpaths live path effect although technically that creates a compound path.

Menu>Extensions>Generate from Path>Interpolate creates a group, rather than a compound path, it seems here.

^I'd go by draw circle one, duplicate it, scale up, select both, combine, add interpolate subpaths lpe,
and, preferably break apart.
Although that cannot have exponential growth between the sizes as with the extension, which, creates groups.