document.write( "Question 816550: (3^(-1)X^(3)Y^(-5))(3^(-1)Y^(-2))^-2 \r
\n" ); document.write( "\n" ); document.write( "Thannkyou for your help. I tried distributing the -2 first and then keep coefficients and add exponents but i am lost. \n" ); document.write( "

Algebra.Com's Answer #491635 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%283%5E%28-1%29X%5E%283%29Y%5E%28-5%29%29%283%5E%28-1%29Y%5E%28-2%29%29%5E-2+\"$
\n" ); document.write( "According to the order of operations (aka PEMDAS) we should start with the exponents (since nothing can be done within either set of parentheses). To raise the expression to the -2 power we use a rule for exponents, $\"%28ab%29%5En+=+a%5En+%2A+b%5En\"$ , which tells us that raising a multiple-factor term to a power, you raise each factor to that power:
\n" ); document.write( "

\n" ); document.write( "To raise the powers of a power we use another rule for exponents, $\"%28a%5En%29%5Em+=+a%5E%28n%2Am%29\"$ :
\n" ); document.write( " $\"%283%5E%28-1%29X%5E%283%29Y%5E%28-5%29%29%283%5E2%29%28Y%5E4%29+\"$
\n" ); document.write( "All that is left is multiplying. For this we use another rule for exponents, $\"a%5En+%2A+a%5Em+=+a%5E%28n%2Bm%29\"$ . We will use this on the 3's and the Y's:
\n" ); document.write( " $\"3%5E%28%28-1%29%2B2%29X%5E%283%29Y%5E%28%28-5%29%2B4%29+\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"3%5E%281%29+X%5E%283%29Y%5E%28-1%29+\"$
\n" ); document.write( "or
\n" ); document.write( " $\"3x%5E3%2Fy\"$

\n" ); document.write( "P.S. While the $\"%28ab%29%5En+=+a%5En+%2A+b%5En\"$ property may look like a Distributive Property, it is not. \n" ); document.write( "

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