Does saying a prayer out loud, have any greater power or standing than saying a prayer privately in one’s mind?

This is an interesting question and the answer is that it will depend on how that shapes the intention and inner conviction of the person praying. We can tell you, as a rule of thumb, when you say something out loud it is typically done with greater conviction and often some preparation to get one’s thoughts in order and to have more attention to detail, the precise wording, and hold further the expectation that because you are giving it extra emphasis, this is more than an idle gesture but one of significance that goes along with the act of making a public declaration, so to speak. Even if one is out in nature and by oneself, stating the prayer out loud in this way is a bold and direct demonstration that you are wanting this to be acted on and for it to be effective. So what we are saying is that this is not all or nothing, one way or another, being good or bad or all-important but that, as a general rule, stating prayers out loud will add some extra oomph, some extra energy because the intensity of the intention one his holding will likely be greater with a spoken declaration and, in fact, that is an effective way for many to add some extra prayer power to their offerings, to say them out loud for that reason. We are not inviting people to engage in a shouting contest here, but only speaking to the human condition, what human nature brings to the party, and how most people typically think and feel. Simply saying something out loud will take a bit more time than thinking it in one’s mind or reading it from a prayer book, for example, which might take place at lightning speed but when spoken, the person will go slower and then be lingering over the words a bit more and will be more in touch with what they are saying and in tune with it simply by pondering it for a bit longer interval. So this is simply a consequence of human physicality but "intention is intention" and that is what we follow, so the more you put into the act of prayer to empower it, the greater energy we will have, to use to act on that prayer request to bring about the greatest possible benefit.