What is the largest number among the following?1. \(\left(\dfrac{1}{2}

1.	What is the largest number among the following?1. \(\left(\dfrac{1}{2}\right)^{-6}\)2. \(\left(\dfrac{1}{4}\right)^{-3}\)3. \(\left(\dfrac{1}{3}\right)^{-4}\)4. \(\left(\dfrac{1}{6}\right)^{-2}\)
Answer» Correct Answer - Option 3 : \(\left(\dfrac{1}{3}\right)^{-4}\) \({\left( {\frac{1}{2}} \right)^{ - \;6}} = \frac{1}{{{{\left( {\frac{1}{2}} \right)}^6}}} = \frac{1}{{\frac{1}{{64}}}} = 64\) \({\left( {\frac{1}{4}} \right)^{ - \;3}} = \frac{1}{{{{\left( {\frac{1}{4}} \right)}^3}}} = \frac{1}{{\frac{1}{{64}}}} = 64\) \({\left( {\frac{1}{3}} \right)^{ - \;4}} = \frac{1}{{{{\left( {\frac{1}{3}} \right)}^4}}} = \frac{1}{{\frac{1}{{81}}}} = 81\) \({\left( {\frac{1}{6}} \right)^{ - \;2}} = \frac{1}{{{{\left( {\frac{1}{6}} \right)}^2}}} = \frac{1}{{\frac{1}{{36}}}} = 36\) ∴ Answer is Option 3

What is the largest number among the following?1. \(\left(\dfrac{1}{2}\right)^{-6}\)2. \(\left(\dfrac{1}{4}\right)^{-3}\)3. \(\left(\dfrac{1}{3}\right)^{-4}\)4. \(\left(\dfrac{1}{6}\right)^{-2}\)

Answer» Correct Answer - Option 3 : \(\left(\dfrac{1}{3}\right)^{-4}\)

\({\left( {\frac{1}{2}} \right)^{ - \;6}} = \frac{1}{{{{\left( {\frac{1}{2}} \right)}^6}}} = \frac{1}{{\frac{1}{{64}}}} = 64\)

\({\left( {\frac{1}{4}} \right)^{ - \;3}} = \frac{1}{{{{\left( {\frac{1}{4}} \right)}^3}}} = \frac{1}{{\frac{1}{{64}}}} = 64\)

\({\left( {\frac{1}{3}} \right)^{ - \;4}} = \frac{1}{{{{\left( {\frac{1}{3}} \right)}^4}}} = \frac{1}{{\frac{1}{{81}}}} = 81\)

\({\left( {\frac{1}{6}} \right)^{ - \;2}} = \frac{1}{{{{\left( {\frac{1}{6}} \right)}^2}}} = \frac{1}{{\frac{1}{{36}}}} = 36\)

∴ Answer is Option 3