Soit \(a,b>0\) et \(p,q\in \mathbb{R}\). Simplifier les expressions suivantes.

1. \(\exp\bigl(p\log(a)+q\log(b)\bigl)\)
2. \(\exp\big(p\big(\log(a)-\log(b)\big)+\log(b)(p+q)\big)\)
3. \(\exp\big(p\log(ab^{-1})+\log(b^{p+q})\big)\)
4. \(\exp\big(q\log\big(\frac{b}{a}\big)+\log(a^q)+p\log(a)\big)\)