The question of whether to use the singular or plural form of a verb in a sentence can be complicated by the distracting presence of a prepositional phrase—one that includes a preposition such as of, in, or to followed by a noun directly or after one or more an intervening verbs and/or adjectives. But as the following examples demonstrate, such a phrase should (with a key exception) be disregarded when identifying which noun the sentence’s key verb should agree with.
1. The rapid and almost ubiquitous deployment of smartphone technologies across the globe has/have put sophisticated technology in the hands of consumers.
The multiplicity of nouns preceding has—deployment, technologies, globe—can throw a writer off, but the noun in a prepositional phrase (such as in “of smartphone technologies” or “across the globe”) is irrelevant, so the first in series of nouns in this sentence (“deployment . . . has”) is the pertinent one: “The rapid and almost ubiquitous deployment of smartphone technologies across the globe has put sophisticated technology in the hands of consumers.”
2. There is/are, however, a set of technologies and innovations that have already reached a point where they are robust enough to have real-world applicability.
This sentence also features a distracting prepositional phrase, but it follows the key verb, rather than preceding it, as the one in the preceding example does, so the writer may not recognize the applicability of the previously mentioned rule; the pairing is “is . . . a set,” not “are . . . technologies and innovations”: “There is, however, a set of technologies and innovations that have already reached a point where they are robust enough to have real-world applicability. (Notice, however, that the subsequent verbs have and are apply to “technologies and innovations” rather than set, so they are correct in plural form.)
3. A number of factors have led to the increasing use of technology in relation to regulatory compliance.
Note, however, an exception to the rule about the irrelevance of prepositional phrases in noun-verb agreement—when the prepositional phrase follows the phrase “a number”; in that case, the more substantial noun in the prepositional phrase, rather than the vague word number, is pertinent: “A number of factors have led to the increasing use of technology in relation to regulatory compliance.”
You can test the exception by realizing that “a number of” can be replaced with the adjective many; the correct form of the verb following “many factors” is obvious. (This post provides a more detailed discussion of the issue.)