let $p$ and $q$ are two exponents such that $p$ is the conjugate exponent of $q$ , I can't get a difference between the two following notation $ \| .\|_{q}^{q}$ and $ \| .\|_{q}$, for example in the solution of this exercice ,Exercice 5 , The Author used two following identities:
$$\|f\|_p^p=\int_{\mathbb{R}}|g(x)|^{p+pq-2p}dx=\|g\|_q^q \tag{1}$$
$$T(f)=\int_{\mathbb{R}}|g|^q=\|g\|_q^q \tag{2}$$
How $(1)$ and $(2)$ are same ? and What is the difference between $ \| g\|_{q}^{q}$ and $ \| g\|_{q}$ ?