KrumpsBrother is dead on-point here.
Chemical control is ultimately the easiest and surest method of dealing with prickly-pear.
We've spent years and years on controlling these things on our property with good results with spraying easily over any other method.
Grazon P+D was mentioned and it will work. For years we used a mixture of Dow Remedy @1 pint and Grazon P+C (P+D's stronger and more expensive alternative) @1 quart to a 55 gallon tank load as a multipurpose mix for pear as well as mesquite and cedar and jubu. Remedy is very expensive but all-powerful too.
But, we found that a 1 pint each mix of Remedy/P+C/P+D would work as well for a little less money. We spot sprayed from a tractor mounted 55-gallon drum/pto pump set-up and it works fantastic.
We kill 90% of everything we hit and by spot spraying we can control what else is affected. Prickly-pear are odd though. You can cover a pasture accurately and see a wide variety of results. Some pear will begin to turn relatively soon...a week or a month. Others will take months to show signs of the application. Therefore, it's a good idea to hit a pasture as well as possible and wait until the next year to really guage the results. Don't go back in a month a spend a wad on more spray to hit plants that aren't showing distress yet.
You essentially control them as much as you can afford to. As expensive as these chemicals are, you should determine what you want to do (wipe them out...or...clear a particular area...etc) buy and apply accordingly, and then give them some time do their job.