Expense is used only as a noun: A new highway was built at great expense.
Price: the cost of things in shops etc.: The price is rather high, can’t you drop (=reduce) it a bit? · What price did he ask? It is also used more generally: James was famous, but he paid a high price for his success.
The value of something is what it is worth, and might be different from its cost: I bought this record for $5 and now it’s worth $100. · A man who knows the price of everything and the value of nothing (Oscar Wilde’s definition of a cynic)
A valuable thing is worth a lot of money or has great value for some other reasons: She made some very valuable suggestions.
The common opposite of valuable is worthless:
What he writes is completely worthless rubbish.
Valueless is more formal: I’m sorry to tell you these paintings are valueless.
Something that is priceless has a value so high that you cannot express it in terms of money: a collection of priceless paintings. Invaluable is used more generally to mean extremely useful: Thank you for your invaluable help.
Notice that valid and its opposite invalid do not refer to the value of something, but to whether it is correct or legally acceptable: a valid ticket; an invalid argument.
