document.write( "Question 725451: simplify each number\r
\n" ); document.write( "\n" ); document.write( "64^3.5 \n" ); document.write( "
Algebra.Com's Answer #444235 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
First let's write the exponent as a fraction:
\n" ); document.write( "\"64%5E%28%287%2F2%29%29\"
\n" ); document.write( "In general a fractional exponent can be written in radical form in two ways:
\n" ); document.write( "\"a%5E%28%28m%2Fn%29%29+=+root%28n%2C+a%5Em%29+=+%28root%28n%2C+a%29%29%5Em\"
\n" ); document.write( "So we can rewrite \"64%5E%28%287%2F2%29%29\" as
\n" ); document.write( "\"root%282%2C+64%5E7%29\"
\n" ); document.write( "or
\n" ); document.write( "\"%28root%282%2C+64%29%29%5E7\"
\n" ); document.write( "(Note: These are square roots. We often don't bother writing the 2 because if there is no number in that position that it is assumed that it is a 2.)

\n" ); document.write( "Now we have to ask ourselves, which looks easier? The first one where we raise 64 to the 7th power and then find a square root? Or the second one where we find the square root of 64 and then raise that to the 7th power. I think you'll agree that since the square root of 64 is a well-known whole number, the second one is easier.
\n" ); document.write( "\"%28root%282%2C+64%29%29%5E7\"
\n" ); document.write( "Since the square root of 64 is 8 this becomes:
\n" ); document.write( "\"8%5E7\"
\n" ); document.write( "I'll leave it up to you to multiply this out. \n" ); document.write( "
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