title: Are 2^n and n*2^n in the same time complexity?
body: <p>Resources I've found on time complexity are unclear about when it is okay to ignore terms in a time complexity equation, specifically with non-polynomial examples. </p>
  
  <p>It's clear to me that given something of the form n<sup>2</sup> + n + 1, the last two terms are insignificant. </p>
  
  <p>Specifically, given two categorizations, 2<sup>n</sup>, and n*(2<sup>n</sup>), is the second in the same order as the first? Does the additional n multiplication there matter? Usually resources just say x<sup>n</sup> is in an exponential and grows much faster... then move on.</p>
  
  <p>I can understand why it wouldn't since 2<sup>n</sup> will greatly outpace n, but because they're not being added together, it would matter greatly when comparing the two equations, in fact the difference between them will always be a factor of n, which seems important to say the least.</p>