Your question on how to estimate the age of Opuntia cactus was quite intriguing to me, after some weekend research the following study seemed most appropriate:
Growth Rate and Life Span of a Prickly Pear Cactus, Opuntia engelmannii, in the Northern Sonoran Desert
Author(s): Janice E. Bowers
Source: The Southwestern Naturalist, Vol. 41, No. 3 (Sep., 1996), pp. 315-318
Published by: Southwestern Association of Naturalists
Stable URL: http://www.jstor.org/stable/30055130
Accessed: 08-08-2017 14:44 UTC
They set some qualifiers for a couple of score cacti to study, which primarily included the following:
- Origin of the plant was apparent; the plant was not so old that its original plant parts had rotted away.
- The plant had no apparent rotting, disease damage, or other obvious issues that would reduce its size or slow its growth rate.
There was no apparent evidence of infestation, or animals using the cactus plants as a home or den.
The study found did produce a formula for estimating the age of a plant based on the number of cladodes it had, and this formula seems to relate to other areas in the southwestern USA, and across other species of Opuntia. There is an average 20% loss rate of cladodes each year. I encourage you to read the 4-page article, see link in source reference above.
The following graph is the simplest way to gauge an Opuntia cactus' age:
Finally, the Opuntia you have pictured is relatively old and without some pictures of the base and poking around in the dirt around the roots it's my best guess is it is over 2, perhaps 3 decades old.