In a boutique, items were put in a showcase, and each was assigned a price for January. Each month after that, the price was 10 percent less than the price for the previous month. What is the ratio of the price of an item in April to the price of the same item in January? Express your answer as a common fraction.
Let the original price = P
Every month, the price of the item is just 90% = .9 of the previous month
So........the price in April = P (.9)^4
So the ratio of the price of an item in April to the price of that item in January =
______ = (.9)^4 = 6561 / 10000