Editing 2010 AMC 8 PROBLEMS/PROBLEM 24

Solution 4

We can use simplifying methods to help us solve this problem. 2 to the 24th power can be written as: (2^6)^4 5 to the 12th power can be written as: (5^3)^4 10 to the 8th power can be written as: (10^2)^4 Now we can see which one is the biggest. 2^6 power is 64, 5^3 power is 125, and 10^2 is 100. Now, we can sort them out. We get that 2^24 power is the smallest, 10^8 power is the next one, and 5^12 power is the biggest. Notice that we factored 4 out of all of them. This is because all of the powers were multiplies of 4. Hence, the answer to problem 24 is .

~aoh11