document.write( "Question 717542: what is 512^-1/3 convert into radical notation
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Algebra.Com's Answer #440334 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"512%5E%28-1%2F3%29\"
\n" ); document.write( "If you have trouble with negative and/or fractional exponents, I have found that it can be helpful to factor the exponent in a special way:
  1. If the exponent is negative, factor out -1.
  2. If the exponent is a fraction and its numerator is not 1, then factor out the numerator.
Using this on your expression...
\n" ); document.write( "1. The exponent is negative so we factor out -1:
\n" ); document.write( "\"512%5E%28%28-1%29%2A%281%2F3%29%29\"
\n" ); document.write( "2. The exponent is a fraction. But its numerator is a 1 so we do nothing.

\n" ); document.write( "Once the exponent is factored this way, each factor tells you an operation to perform:
  • A factor of -1 in the exponent means we should find a reciprocal.
  • A factor that is a fraction (with a numerator of 1) means find a root of the kind specified by the denominator.
  • If there is another factor it will be a positive whole number which means what it usually means.
And these operations can be done in any order! So choose an order that looks easier.

\n" ); document.write( "So for:
\n" ); document.write( "\"512%5E%28%28-1%29%2A%281%2F3%29%29\"
\n" ); document.write( "we will find a reciprocal and find a cube root. Which should we start with? If we start with the reciprocal we get a fraction (since the reciprocal of 512 is 1/512). Then we would be finding a cube root of a fraction. Or we could start with the cube root and then find the reciprocal. This second path looks easier to me.

\n" ); document.write( "After a little effort we should be able to figure out that \"8%5E3+=+512\" so the cube root of 512 is 8. And the reciprocal of 8 is 1/8. So:
\n" ); document.write( "\"512%5E%28-1%2F3%29+=+512%5E%28%28-1%29%2A%281%2F3%29%29+=+1%2F8\"
\n" ); document.write( "Since 512 was a perfect cube we never really needed radical notation. But we could use it anyway:
\n" ); document.write( "\"512%5E%28-1%2F3%29+=+512%5E%28%28-1%29%2A%281%2F3%29%29+=+1%2Froot%283%2C+512%29+=+1%2F8\"
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