Is this a proper way of answering the question? I thought that forward rate such as “3y2y” does not require us to use exponent because the rate for the 2 years is already implied.
So the “proper way” I thought would be: 1.027^3 x 1.044
Yes, this is a proper way to answer the question. The 3yr2yr forward rate would be the implied annual rate 3 years from now for two years. So you need to square it and then multiply it by the 3 year spot to the third power to get the five year spot to the fifth power. You then raise that computed rate to the 1/5 exponent to get your answer.