I want to simplify an expression,
((1 + beta1 E^(d - r1 t))^(-1/beta1))^beta1 // Simplify // Normal
But it didn't work. Would you like to help me? Thanks.
Marco, Your way works. But if beta1>0?
In[22]:= eq5 = (D[X1[t], t]/X1[t] - r1/beta1*(1 - (X1[t]/K1)^ beta1)) /. {X1 -> ((K1*(1 + beta1*Exp[d - r1*#1])^(-1/ beta1)) &)} // Factor // FullSimplify // Normal Out[22]= (E^d r1)/( beta1 E^d + E^( r1 t)) + ((-1 + ((1 + beta1 E^(d - r1 t))^(-1/beta1))^ beta1) r1)/beta1 In[44]:= eq6 = Simplify[eq5, beta1 > 1] Out[44]= 0
The problem is when 1 + beta1 E^(d - r1 t) < 0, because if you "simplify" the powers the value changes:
1 + beta1 E^(d - r1 t) < 0
values = {d -> r1 t + Log[4], beta1 -> -1/2}; eq5 /. values PowerExpand[eq5] /. values
It is not always true that (a^b)^(1/b) is the same as a.
(a^b)^(1/b)
a
What do you expect the result to be? Do you implicitly make any further assumptions?
Simplify[((1 + beta1 E^(d - r1 t))^(-1/beta1))^beta1, Assumptions -> beta1 > 1] (*1/(1 + beta1 E^(d - r1 t))*)
Cheers,
Marco
