document.write( "Question 625265: (^13sqrt2x^6y)^5 rewrite with rational exponents \n" ); document.write( "
Algebra.Com's Answer #393451 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"^13sqrt\"???
\n" ); document.write( "Do you mean \"%28root%2813%2C+2x%5E6y%29%29%5E5\"? If yes, then
  • This is not a square root. It is a 13th root.
  • The 13 is not an exponent even though it may look like one. It is the \"index\" of the radical which indicates which kind of root it is.
  • To post problems with roots that are not square roots, do not use \"sqrt\" to describe it. For this problem you could either:
    • Use some English like: \"(the 13th root of (2x^6y))^5\"; or
    • Teach yourself the syntax used by algebra.com to display these mathematical expressions. Click on the \"Show Source\" link above to see what I typed to get the 13th root to display. Look for the expressions inside the sets of three braces: {...}
      \n" ); document.write( "

\n" ); document.write( "Radical expressions can be replaced with fractional/rational exponents. The fraction (or ratio) to use when replacing a radical with a rational exponent is 1 over the index of the radical. So to replace our radical with a rational exponent we will use 1/13:
\n" ); document.write( "\"%28%282x%5E6%2Ay%29%5E%281%2F13%29%29%5E5\"
\n" ); document.write( "Now we just use the power of a power rule for exponents (i.e. multiply the exponents:
\n" ); document.write( "\"%282x%5E6%2Ay%29%5E%285%2F13%29\"

\n" ); document.write( "P.S. Square roots do not have a visible index. For example: \"sqrt%282%29\". A missing/invisible index is considered to be a 2. IOW, \"sqrt%282%29\" means the same thing as \"root%282%2C+2%29\". So the rational exponent for square roots is 1/2. \n" ); document.write( "
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