Why doesn't RPMs for fedora or suse work in mandriva?

Those are installation packages. You don't run them, but instead run your package manager or the rpm command.
see: man rpm

Each package manager maintains a database of what is installed so that it can determine what additional SW is required when you install a new package. (i.e. the package manager resolves all the dependencies.

You can install an rpm package on any machine that uses rpm---or on a .deb-type system using alien. The only issue will be that YOU have to resolve all the dependencies.

Always try your package manager first.

If I understand your question correctly, you want to install one or more rpm package(s) intended for use with Fedora or Suse on a Mandriva installation. Since all three distributions use the rpm file format with their software managers, it is possible to do, but may be fraught with problems.

Perhaps a brief explanation is in order. Each Linux distributor selects which software will be included in the distribution, and may even make modifications to correct any conflicts. They decide how the software will be separated into rpm packages, then package it for use with their distribution. An rpm file contains not only the software itself, but a list of other packages containing the software it depends on, and sometimes scripts which must be run to properly configure it at install time. The dependency list (and possibly any install time scripts) for any given program will be different for each distribution, because the package file names will be different and the way the software was separated into packages may differ as well.

When a third party vendor provides their software in an rpm file (e.g.: Adobe Acrobat Reader), they will usually specify which function libraries will be needed by their package, and they will package their software with no external dependencies. In this way, you can download their package and install it successfully to a wide variety of distributions.

As a final note, all three distributors you mentioned in the quote above include the widest possible range of software packaged for use with their distribution. If (as your inquiry suggests) you are using Mandriva, they provide an outstanding range of software on their ftp mirrors. If you have not yet configured a set of Internet Software Media Sources on your system for use with the Mandriva Package Management System you should do so. You may then find the software you need, ready to install and use with no problems. I have written an article to help others with this task on my LQ Blog.

HTH,