Question

While ordering these four numbers from least to greatest: $5^{36}$, ${10}^{51}$, ${17}^{35}$, ${31}^{17}$, which is the 3rd number?

• A. 5³⁶
• B. 10⁵¹
• C. 17³⁵
• D. 31¹⁷

Answer 1

The correct option is C

17³⁵

${10}^{51}>9^{51}=3^{102}={27}^{34}>{17}^{35}>{16}^{35}={32}^{28}>{31}^{17}>{25}^{18}=5^{36}.$
So the ordering is $5^{36}<{31}^{17}<{17}^{35}<{10}^{51}$.