document.write( "Question 214257This question is from textbook
\n" ); document.write( ": (4x to the negative one power, y to the 1/3 power) to the 3/2 power
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\n" ); document.write( " (xy) to the 3/2 power\r
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\n" ); document.write( "\n" ); document.write( "I really need help with this one, I don't understand it at all... \n" ); document.write( "
Algebra.Com's Answer #161851 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "When working with exponents there are several key things to understand:
  • The rules for exponents:
    1. \"a%5Ep+%2A+a%5Eq+=+a%5E%28p%2Bq%29\"
    2. \"a%5Ep%2Fa%5Eq+=+a%5E%28p-q%29\"
    3. \"%28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29\"
    4. \"%28a%2Ab%29%5Ep+=+a%5Ep+%2A+b%5Eq\"
    5. \"%28a%2Fb%29%5Ep+=+%28a%5Ep%29%2F%28b%5Ep%29\"
    6. \"a%5E%281%2Fp%29+=+root%28p%2C+a%29\"
    7. \"a%5E%28-p%29+=+1%2F%28a%5Ep%29\"
    8. \"a%5E0+=+1\" (if a is not zero)
  • The rules above apply regardless what the exponents are. They work on positive, negative, zero and fractional exponents.
  • As with most things in Math, the rules work in both directions.
  • Since exponents are, in essence, a form of multiplication and since multiplication is commutative, it rarely makes a difference the order you apply these rules (as long as you apply them correctly!).

\n" ); document.write( "So there are often many ways to simplify an expression with exponents. Here's a couple of possible solutions:

\n" ); document.write( "Solution #1:
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\n" ); document.write( "1) Using rule #4 on the numerator and on the denominator:
\n" ); document.write( "\"%28%284x%29%5E%28-3%2F2%29%2Ay%5E%281%2F2%29%29%2F%28x%5E%283%2F2%29%2Ay%5E%283%2F2%29%29\"
\n" ); document.write( "2) Using rule #4 on the \"4x\":
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\n" ); document.write( "3) Using rule #2 on the x's and y's\"
\n" ); document.write( "\"4%5E%28-3%2F2%29%2Ax%5E%28%28-3%2F2+-+3%2F2%29%29%2Ay%5E%28%281%2F2+-+3%2F2%29%29\"
\n" ); document.write( "which simplifies to
\n" ); document.write( "\"4%5E%28-3%2F2%29%2Ax%5E%28-3%29%2Ay%5E%28-1%29\"
\n" ); document.write( "4) To simplify the \"4%5E%28-3%2F2%29\", if you don't see it otherwise, factor the exponent:
\n" ); document.write( "\"4%5E%283%2A%281%2F2%29%2A%28-1%29%29%2Ax%5E%28-3%29%2Ay%5E%28-1%29\"
\n" ); document.write( "5) Then we can use rule #3 (from right to left) twice:
\n" ); document.write( "\"%28%284%5E3%29%5E%281%2F2%29%29%5E%28-1%29%29%2Ax%5E%28-3%29%2Ay%5E%28-1%29\"
\n" ); document.write( "6) Since 4^3 = 64:
\n" ); document.write( "\"%28%2864%29%5E%281%2F2%29%29%5E%28-1%29%29%2Ax%5E%28-3%29%2Ay%5E%28-1%29\"
\n" ); document.write( "7) Using rule #6 on \"64%5E%281%2F2%29\"\"
\n" ); document.write( "\"%28%28sqrt%2864%29%29%5E%28-1%29%29%2Ax%5E%28-3%29%2Ay%5E%28-1%29\"
\n" ); document.write( "8) Since \"sqrt%2864%29+=+8\":
\n" ); document.write( "\"8%5E%28-1%29%2Ax%5E%28-3%29%2Ay%5E%28-1%29\"
\n" ); document.write( "9) Using rule #7 on \"8%5E%28-1%29\":
\n" ); document.write( "\"%281%2F8%29%2Ax%5E%28-3%29%2Ay%28-1%29\"
\n" ); document.write( "At this point we could stop, unless you are not supposed to have negative exponents, In this case we use rule 9 on the x's and y's giving:
\n" ); document.write( "\"1%2F%288x%5E3y%29\"

\n" ); document.write( "Solution #2:
\n" ); document.write( "
\n" ); document.write( "1) Use Rule #5 (from right to left) on the entire fraction (since the exponents on the numerator and denominator are the same):
\n" ); document.write( "\"%28%28%284x%29%5E%28-1%29%2Ay%5E%281%2F3%29%29%2F%28xy%29%29%5E%283%2F2%29%29\"
\n" ); document.write( "2) Using rule #4 on the \"4x\":
\n" ); document.write( "\"%28%284%5E%28-1%29%2Ax%5E%28-1%29%2Ay%5E%281%2F3%29%29%2F%28xy%29%29%5E%283%2F2%29\"
\n" ); document.write( "3) Using rule #2 on the x's and y's\"
\n" ); document.write( "\"%284%5E%28-1%29%2Ax%5E%28%28-1-1%29%29%2Ay%5E%28%281%2F3-1%29%29%29%5E%283%2F2%29\"
\n" ); document.write( "which simplifies to
\n" ); document.write( "\"%284%5E%28-1%29%2Ax%5E%28-2%29%2Ay%5E%28-2%2F3%29%29%5E%283%2F2%29\"
\n" ); document.write( "4) Using rule #3:
\n" ); document.write( "\"4%5E%28-3%2F2%29%2Ax%5E%28-3%29%2Ay%5E%28-1%29\"
\n" ); document.write( "And the rest is the same as the first solution.... \n" ); document.write( "
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