Question

Here is a tricky but fun problem involving large exponents or high powers.

Which of the following numbers is greater, 31¹³ or 17¹⁷?​

Answer 1

17 ^17

Explanation:

Its power is bigger

You shouldn't be tricked because 31 is more than 17

Answer 2

Explanation:

Notice that 31 + 1 = 32 = 2⁵ and 17 - 1 = 16 = 2⁴.

31¹³ < 32¹³

= (2⁵)¹³ = 2⁶⁵

= 2(2⁴)¹⁶ = 2 * 16¹⁶

< 16¹⁷ < 17¹⁷.

Hence 17¹⁷ is greater than 31¹³.