De-trending variables in a DSGE model

[PhD_econ]

In this paper (https://www.sciencedirect.com/science/article/abs/pii/S0304387822001791) the authors de-trend their model’s variables by A^{\frac{1}{1-\alpha}} where A_t represents the level of technology or total factor productivity (TFP). I don’t understand how do they get the exponent {\frac{1}{1-\alpha}} ?
Thanks

[jpfeifer]

See

Explicitly specified trend to TFP (not labor augmenting)

The reason I focused on labor-augmenting technology is that a balanced growth path requires technology to be represented in that form. Thus, generally TFP growth can be written as labor augmenting growth (usually due to the use of a Cobb-Douglas function). Y_t=A_t K_t^\alpha N_t^{1-\alpha}=K_t^\alpha\left(A_t^{1/(1-\alpha)} N_t\right)^{1-\alpha}=K_t^\alpha\left(\tilde A_t N_t\right)^{1-\alpha}

[PhD_econ]

Thank you !