Update SQL Server Table Row by row from values of other table with joins

I have 3 tables.

Table Product

Product_ID | Review_date |
1          | 01/01/2018    |
2          | 01/01/2018    |
3          | 01/01/2018    |
4          | 01/01/2018    |

Table Inventory
Inventory_ID  | Product_ID  | Location_ID
1             |        2    | 1    |
2             |        2    | 3    |
3             |        3    | 4    |
4             |        1    | 4    |

Table Location
Location_ID| Review_date |
1          | 04/02/2018    |
2          | 06/03/2018    |
3          | 01/05/2018    |
4          | 08/28/2018    |

UPDATE The product table set of product information. The inventory table has information about places where the products are available, One product can have multiple inventories and a product can have no inventories. The location table has unique list of all the possible locations. The review date in the location table is often updated.

I want to update the review date in the product table for each product ID and selecting the max(review_date) from location table for each product ID. Because a product can have multiple inventories and locations assigned to it. I want the recent date the product's location is updated.

Expected result

Table Product

Product_ID | Review_date |
1          | 08/28/2018    |  this prod id in inventory has loc id 4. 
2          | 04/02/2018    |  two inv records for the product so max date
3          | 08/28/2018    |
4          | 01/01/2018    |  no inv record. so leave it as such


UPDATE  P
SET     P.review_date = L.Inventory_review_date
FROM    Product AS P
CROSS APPLY
        (
        select  top 1 inventory_review_Date
        from    Location as L, Inventory as I, PRODUCT as P
        where   L.Location_ID = I.Inventory_ID and P.Product_ID = I.Product_ID
        order by
                L.Inventory_Review_date desc
        ) as L  

I tried something like this in different ways but i dont seem to get it. Any help appreciated. TIA