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SMO 2016 Senior Round 1 Question 6

SMO · SMO 2016 Senior Round 1

Question 6

Which of the following is the greatest?
  1. $\sqrt{\frac 16}$
  2. $\left(\frac 1{218}\right)^{1/6}$
  3. $\left(\frac 1{15}\right)^{1/3}$
  4. $\left(\frac 17\right)^{1/3}\left(\frac 15\right)^{1/6}$
  5. $\left(\frac 18\right)^{1/4}\left(\frac 13\right)^{1/3}$