Validity of exponentiation in a polynomial time reduction
The proof as presented in the paper is not conclusive.

However, the stated result itself is correct. It can easily be derived by slightly changing the reduction and by using SUBSET PRODUCT instead of SUBSET SUM.

A useful link for the SUBSET PRODUCT problem:
https://cs.stackexchange.com/questions/7907/is-the-subset-product-problem-np-complete