Question #80447

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Answer 1 · 2017-08-24T00:36:21

#( - e^(lnx) x^3 e^(1-x) )^2 = x^8 e^(2-2x)#

#( - e^(lnx) x^3 e^(1-x) )^2#

First simplify what is inside the parentheses, note that #e^lnx=x#

#= ( -x*x^3*e^(1-x) )^2#

# = ( -x^4e^(1-x) )^2#

Distribute the exponent among what is inside the base of the exponent:
# = (-1)^2 * (x^4)^2 * (e^(1-x))^2#

Simplify:

# = x^8 e^(2-2x)#