Estimate on average with weight

Question

Let $B_{2R}=B(x,2R)$ be the ball of radius $2R$ centered at $x$ and $v=log\,u$ for some positive function $u$ defined on $B_{2R}$. Denote by $v_{B_{2R}}=\frac{1}{w(B_{2R})}\int_{B_{2R}}v(x)w(x)\,dx$, where $w(B_{2R})=\int_{B_{2R}}w(x)\,dx$. Then \begin{align*} \frac{1}{w(B_{2R})}\int_{B_{2R}}e^{-p_0 v}w(x)\,dx\cdot\frac{1}{w(B_{2R})}\int_{B_{2R}}e^{p_0 v}w(x)\,dx\\ =\frac{1}{w(B_{2R})}\int_{B_{2R}}e^{(p_0 v-p_0 v_{B_{2R}})}w(x)\,dx\cdot\frac{1}{w(B_{2R})}\int_{B_{2R}}e^{(p_0 v_{B_{2R}}-p_0 v)}w(x)\,dx \end{align*} Can you kindly help me how to get the above equality. Thanking you.