\documentclass{article}

\begin{document}

$$\Phi(x) = \left( \sum_{Vertex\;v} c_v \Phi_v(x)
        \right)^{\int_\Omega a \, dx}$$

$$\Phi(x) = \left( \sum_{Vertex\;v} c_v \Phi_v(x) + 
        \sum_{Edge\;e} \sum_{i} c_{e,i} \Phi_{e,i}(x)
        \right)^{\int_\Omega a \, dx}$$

$$\Phi(x) = \left( \sum_{Vertex\;v} c_v \Phi_v(x) + 
        \sum_{Edge\;e} \sum_{i} c_{e,i} \Phi_{e,i}(x) +
        \sum_{Face\;f} \sum_{i} c_{f,i} \Phi_{f,i}(x)
        \right)$$

$$\Phi(x) = \left( \sum_{Vertex\;v} c_v \Phi_v(x) + 
        \sum_{Edge\;e} \sum_{i} c_{e,i} \Phi_{e,i}(x) +
        \sum_{Face\;f} \sum_{i} c_{f,i} \Phi_{f,i}(x)
        \right)^{\int_\Omega a \, dx}$$

\end{document}

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