Which of the following is the smallest among $ (14)^{\frac{1}{3}}, (12)^{\frac{1}{2}},(16)^{\frac{1}{6}}$ & $(25)^{\frac{1}{12}}$?
Answer & explanation
Correct answer: option 2
Which of the following is the smallest among $ (14)^{\frac{1}{3}}, (12)^{\frac{1}{2}},(16)^{\frac{1}{6}}$ & $(25)^{\frac{1}{12}}$ =
Multiply power by 12 or take the LCM of powers = 12
= (14)1/3 = (14)12/3 = (14)4
= (12)1/2 = (12)12/2 = (12)6
= (25)1/12 = (25)12/12 = (25)1
= (16)1/6 = (16)12/6 = (16)2
So, $(25)^{\frac{1}{12}}$ is the smallest.