$X_1$ and $X_2$ constitute a random sample of size 2 from a population given by $f(x, T)=T\cdot {x^{T-1}}$ for $0<x<1$ and equal to zero elsewhere. If Critical region is $x_1\cdot x_2\geqslant 3/4$ is used to test the null hypothesis $T=1$ against $T=2$, what is the power of this test at $T=2$?
I defined beta as $\mathbb P\{x_1\cdot x_2<3/4 \mid T=2\}$ or equivalently $1-\mathbb P\{x_1\cdot x_2>3/4 \mid T=2\}$. I understand the $f(x_1\cdot x_2)= T^2{x_1^{T-1}}{x_2^{T-1}}$. I used this to calculate the required probability but I am not getting the given answer for $1-\beta$ (the given answer is 0.114).