document.write( "Question 413833: -625^-1/4 \n" ); document.write( "
Algebra.Com's Answer #290568 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
I hope you posted the problem exactly as it was given to you because
\n" ); document.write( "\"-625%5E%28-1%2F4%29\"
\n" ); document.write( "and
\n" ); document.write( "\"%28-625%29%5E%28-1%2F4%29\"
\n" ); document.write( "are not the same thing!! Exponents apply only to whatever is directly in front of them. So in
\n" ); document.write( "\"-625%5E%28-1%2F4%29\"
\n" ); document.write( "the exponent applies only to the 625. In
\n" ); document.write( "\"%28-625%29%5E%28-1%2F4%29\"
\n" ); document.write( "the exponent applies to (-625)

\n" ); document.write( "So \"-625%5E%28-1%2F4%29\" is the same as
\n" ); document.write( "\"-%28625%29%5E%28-1%2F4%29\"
\n" ); document.write( "If you have trouble with negative and/or fractional exponents I find it can be helpful to factor the exponent in a special way:
  1. If the exponent is negative, then factor out -1.
  2. If the exponent is fractional and the numerator is not a 1, then factor out the numerator. For example, if the exponent was 3/4, then factor out the 3: 3*(1/4).

\n" ); document.write( "Factoring your exponent in this way...
\n" ); document.write( "Your exponent is negative wo we will factor out -1:
\n" ); document.write( "\"-%28625%29%5E%28%28-1%29%2A%281%2F4%29%29\"
\n" ); document.write( "Your exponent is fractional but the numerator is 1 so we are finished factoring the exponent. Once factored, each factor of the exponent tells us an operation to perform:
  • The -1, as an exponent, tells us to find a reciprocal.
  • The 1/4, as an exponent, tells us to find a 4th root.

\n" ); document.write( "And since multiplication is Commutative we can do these operations in any order we choose! Since a reciprocal of 625 will create a fraction and since fractions are usually harder to deal with than integers and since \"625+=+5%5E4\" (makingthe 4th root of 625 easy), I choose to do the reciprocal last:
\n" ); document.write( "\"-%28625%29%5E%28%281%2F4%29%2A%28-1%29%29\"
\n" ); document.write( "\"-%28%28625%29%5E%281%2F4%29%29%5E%28-1%29%29\"
\n" ); document.write( "\"-%285%29%5E%28-1%29\"
\n" ); document.write( "\"-%281%2F5%29\" \n" ); document.write( "
\n" );