import re
s = '\\(2 \\, e^{\\left(2 \\, x\\right)} \\sin\\left(2 \\, x\\right) + 2 \\, e^{\\left(2 \\, x\\right)} \\cos\\left(2 \\, x\\right)\\)'
print(re.sub(r'e\^{\\left\((.*?)\\right\)}', r'e^{\1}', s))
aW1wb3J0IHJlCgpzID0gJ1xcKDIgXFwsIGVee1xcbGVmdCgyIFxcLCB4XFxyaWdodCl9IFxcc2luXFxsZWZ0KDIgXFwsIHhcXHJpZ2h0KSArIDIgXFwsIGVee1xcbGVmdCgyIFxcLCB4XFxyaWdodCl9IFxcY29zXFxsZWZ0KDIgXFwsIHhcXHJpZ2h0KVxcKScKcHJpbnQocmUuc3ViKHInZVxee1xcbGVmdFwoKC4qPylcXHJpZ2h0XCl9JywgcidlXntcMX0nLCBzKSk=