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simplifying (x^a)^b

the sage command

var('x alpha beta Lambda mu')
f(x) = ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)
f(x).simplify()

does not give the correct answer g(x)

alpha_x = ((x*f.diff(x)/f).simplify_full()).factor()
g(x) = x^alpha_x

does anyone know why ?

thank you

Philippe

simplifying (x^a)^b

the sage command

var('x alpha beta Lambda mu')
f(x) = ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)
f(x).simplify()

does not give the correct answer g(x)

alpha_x = ((x*f.diff(x)/f).simplify_full()).factor()
g(x) = x^alpha_x

does anyone know why ?

thank you

Philippe

simplifying (x^a)^b( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)

the sage command

var('x alpha beta Lambda mu')
f(x) = ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)
f(x).simplify()

does not give the correct answer g(x)

alpha_x = ((x*f.diff(x)/f).simplify_full()).factor()
g(x) = x^alpha_x

does anyone know why ?

thank you

Philippe