Powerful Order
Powers of numbers might look large, but which of these is the largest...
Age
14 to 16
Challenge level
Problem
List the following three numbers in increasing order:
$$2^{25} 8^8 3^{11}$$
Student Solutions
Answer: $3^{11} < 8^8 < 2^{25}$
We have $8^8= (2^3)^8=2^{24}=(2^2)^{12}=4^{12}> 3^{11}$
So $3^{11}< 8^8$
Also $2^{24}< 2^{25}$ so $8^8< 2^{25}$
So the order is $3^{11} < 8^8 < 2^{25}$