document.write( "Question 643932: Can someone help me with this. Thanks for your time on this.\r
\n" ); document.write( "\n" ); document.write( "1. What is the largest integer power of two that is less than 665?\r
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Algebra.Com's Answer #404768 by KMST(5328) $\"\"$ $\"About$

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.
\n" ); document.write( "If/when I did not remember that,
\n" ); document.write( "I would calculate
\n" ); document.write( " $\"2%5E2=2%2A2=4\"$
\n" ); document.write( " $\"2%5E3=2%2A2%2A2=2%5E2%2A2=4%2A2=8\"$
\n" ); document.write( " $\"2%5E4=2%2A2%2A2%2A2=2%5E3%2A2=8%2A2=16\"$
\n" ); document.write( "and so on, so
\n" ); document.write( " $\"2%5E5=16%2A2=32\"$
\n" ); document.write( " $\"2%5E6=32%2A2=64\"$
\n" ); document.write( " $\"2%5E7=64%2A2=128\"$
\n" ); document.write( " $\"2%5E8=128%2A2=256\"$ and
\n" ); document.write( " $\"2%5E9=256%2A2=512\"$
\n" ); document.write( "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:
\n" ); document.write( "2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,
\n" ); document.write( "and then I would count to find that 512 is the 9th number in that geometric sequence/progression,
\n" ); document.write( "so it is thwe product of $\"2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2\"$ with nine twos, so it's $\"2%5E9\"$ . \n" ); document.write( "

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