An Extension to CES Demand

I am reading a paper with an extended CES final good setting:

• The representative household consists of a continuum of members, indexed by $k$
• $C_{t}=int C_{k, t} d k$
• $C_{k, t}=left(int_{j in Omega_{t}} theta_{k, j}^{frac{1}{eta}} c_{k, j, t}^{frac{eta-1}{eta}} d jright)^{frac{eta}{eta-1}}$, where $theta_{k, j}$ is a utility weight summarized by a CDF $F_{j}left(theta_{k, j}right)$
• Define utility weight for good $j$ at the household level $kappa_{j}left(s_{j, t}right)=int theta_{k, j} d F_{j}left(theta_{k, j}right)$
• Then $C_{t}=left(int_{j in Omega_{t}}left[kappa_{j}left(s_{j, t}right)right]^{frac{1}{n}} c_{j, t}^{frac{eta-1}{eta}} d jright)^{frac{eta}{eta-1}}$

I don’t understand how to derive the last equation? Why can I simply change the order of integration when the inner integral is to a power?

Thanks.