SOLUTION: Can someone help me with this. Thanks for your time on this. 1. What is the largest integer power of two that is less than 665?

Algebra ->  Conversion and Units of Measurement -> SOLUTION: Can someone help me with this. Thanks for your time on this. 1. What is the largest integer power of two that is less than 665?       Log On


   

Question 643932: Can someone help me with this. Thanks for your time on this.
1. What is the largest integer power of two that is less than 665?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I know that 2%5E10=1024, and that helps me figure out that highlight%282%5E9=512%29 is the larges power of 2 with an integer exponent that is less than 665.
If/when I did not remember that,
I would calculate
2%5E2=2%2A2=4
2%5E3=2%2A2%2A2=2%5E2%2A2=4%2A2=8
2%5E4=2%2A2%2A2%2A2=2%5E3%2A2=8%2A2=16
and so on, so
2%5E5=16%2A2=32
2%5E6=32%2A2=64
2%5E7=64%2A2=128
2%5E8=128%2A2=256 and
2%5E9=256%2A2=512
Of course I would not write all that just to calculate 2%5E9. I would just write the results one after the other or one above the other:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,
and then I would count to find that 512 is the 9th number in that geometric sequence/progression,
so it is thwe product of 2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2 with nine twos, so it's 2%5E9.