Well, I have been doing the exercise 2, page 17-18 in this book.

The task is to find phrases and divide them all into 3 groups, Verb Phrases/ Nominal Phrases/ Prepostitional Phrases.

Here comes the whole passage.

Americans are well known for their love of eating out, particuarly at fast-food restaurants. yet, it is worth remembering that 100 years ago, Americans almost always ate home-cooked meals, rarely going out to eat. What were the cases of this dramatic change? Well, the early twentieth century saw great changes in American domestic life that drew people out of their homes and kept them out: the automobile, women in the workforce, the rise of social clubs, and a range of city diversions such as going to the movies or the theatre. Wealthy New Yorkers began the trend by eating out at expensive restaurants and hotels. People who went out in the evenings, for example to the theatre, would often dine out as well. As the American economy grew, more and more people found that they needed to eat out because of work and could eat out because they had more disposable income. In addition, cheaper restaurants opened up. Foreign restaurants grew in number, diversity, and populartiy, with Chinese cuisine making the greatest gains, Cafeterias and diners, both invented in the 1890s, grew in populartiy, and in 1925 Howard Johnson opened his first restaurant. This period also saw the rise of those famous American foods, the hot dog and the hamburger - and with them the founding of the first modern fast food stands. At around the same time, Americans became fond of carbonated drinks. Coca-cola and lemonade were the most popular, though there were (and still are) many other kinds. These drinks were sold in stores and on the streets - like hot dogs and hamburgers. Perhaps it's not surprising, that Americans still enjoy the combination of coca-cola and a hamburger as a quick and easy meal today.
First of all, I have found all answers for the fisrt group, Verb Phrases. But, I found one more (not listed in the answer page): eat out. Why is this phrase not a correct answer?

Secondly, for Prepositional Phrases, I was wondering why (grew) in number is right but (grew) in popularity is not? The same goes for at expensive restaurants and hotels?

Thirdly, why is (women) in the workforce is a prepositional phrase? Why is the whole women in the workforce considered as a nominal one as a whole?
Below are the keys.

Verb Phrases: going out/ drew out of/ keep them out/ dine out/ opened up/ invented in
Nominal Phrases: cooked meals, dramatic change
Prepositional Phrases: of eating out/ at fast-food restaurants/ in the work force/ in number/ in stores/ on the streets
For Nominal Phrases, I have three different questions.

First, if dramatic change is a nominal phrase, is this dramatic change still correct? Why is this removed?

Second, because (this) dramatic change is a nominal one, so how about the whole phrase of the causes of this dramtic change? I think this longer and larger combination functions as a subject and it is okay.

Last, I know that the authors point out only 2 nominal phrases. However, in my opinion, there are more to list. Maybe I have mistaken Nominal Phrase and Noun Phrase. For me, they both refer to one notion. Am I correct?

Can you help me by mentioning which matters you aim to, such as:

For Verb Phrases,...

So, it will be easier for further discussions if needed. Thanks for all helps.