document.write( "Question 405836: 25^-3⁄2 \n" ); document.write( "
Algebra.Com's Answer #286625 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"25%5E%28%28-3%2F2%29%29\"
\n" ); document.write( "If you have trouble with negative and/or fractional exponents I find that it can be helpful to factor the exponent in a certain 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. (You'll see what this means shortly.)

\n" ); document.write( "Let's use this on your exponent:
\n" ); document.write( "1) Your exponent is negative so we will factor out -1:
\n" ); document.write( "\"25%5E%28%28%28-1%29%2A%283%2F2%29%29%29%29\"
\n" ); document.write( "2) Your exponent is fractional and the numerator is 3. So we will factor out 3:
\n" ); document.write( "\"25%5E%28%28%28-1%29%2A3%2A%281%2F2%29%29%29%29\"

\n" ); document.write( "Each factor of the exponent tells you an operation to perform:
  • The -1 as an exponent tells us to find a reciprocal.
  • The 3 as an exponent tells us that we will be cubing (raising to the 3rd power).
  • The 1/2 as an exponent tells us to find a square root.

\n" ); document.write( "Since multiplication is Commutative we can change the order of these factors in any way we want and this changes the order of the operations. So let's try to find an order that looks easiest. A reciprocal of 25 would create a fraction so let's not start by creating a fraction. Cubing 25 is not hard but it would create a fairly large number so let's postpose that, too. A square root of 25 is easy. To me the easiest order is square root, cube, reciprocal. If you like a different order then use that. The three opertions, done in any order and done correctly, will result in the same answer! Using my order we get:
\n" ); document.write( "\"25%5E%28%28%281%2F2%29%2A3%2A%28-1%29%29%29%29\"
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( "\"%28%2825%5E%28%281%2F2%29%29%29%5E3%29%5E%28%28-1%29%29\"
\n" ); document.write( "\"%285%5E3%29%5E%28%28-1%29%29%29%29\"
\n" ); document.write( "\"125%5E%28%28-1%29%29%29\"
\n" ); document.write( "\"1%2F125\" \n" ); document.write( "
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