if Salesforce can maintain and adjusts prices in the pricebook based on exchange rate fluctuation?
The answer is yes. There are two ways it can be done. Be aware that how you implement multiple currencies and create your pricebooks can have an unexpected impact on the results.
It's only if you use Advanced Currency Management that changes in exchange rates will apply to forecasting history for Closed-Won Opportunities. This trickles down to Pricebook since Opportunity Amount is derived from Pricebook, but possibly may not affect the quote of opportunities where the status is not closed-won.
In terms of displaying more than one currency, there are two ways in which they can display in a Pricebook. Here's one, from Help:
Product Currency In multicurrency organizations, the currency that you use for the product. If the product currency differs from the user currency, currency-related fields for opportunities, quotes, and quote line items appear in both currencies. The product’s currency is converted to the user’s currency, and the converted amount appears in parentheses.
Here's the other, more explicit way as taken from the SOAP API Developer Guide:
Use this object to define the default product information for your org. This object is associated by reference with Pricebook2 objects via PricebookEntry objects. The same product can be represented in different price books as price book entries. In fact, the same product can be represented multiple times (as separate PricebookEntry records) in the same price book with different prices or currencies. A product can only have one price for a given currency within the same price book. To be used in custom price books, all standard prices must be added as price book entries to the standard price book.
Note that in the latter example, regardless of whether you're using advanced currency management, when the exchange rate is changed, there would be no impact to any changes in price between multiple currencies for products listed in a pricebook compared to a company's default currency. Those changes would need to be made manually.