document.write( "Question 209838: I need to simplify this expression: 9x^4y^2/3x^2y^5 using positive exponents and I have tried everything and still can't get an answer that makes sense. What is the technique to answer the question? \n" ); document.write( "

Algebra.Com's Answer #158623 by tutor_paul(519) $\"\"$ $\"About$

You can put this solution on YOUR website!
The technique of simplifying exponents is cases like this boils down to 2 methods:
\n" ); document.write( "#1 Multiplying: When two terms have the same base and are multiplied together, the rule is to keep the base and add the exponents. For example:
\n" ); document.write( " $\"%28x%5E2%29%28x%5E3%29=x%5E5\"$
\n" ); document.write( "#2 Dividing: When two terms have the same base and are divided, the rule is to keep the base and subtract the exponents. For example:
\n" ); document.write( " $\"x%5E4%2Fx%5E2=x%5E2\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "Apply these to your problem as follows:
\n" ); document.write( " $\"9x%5E4y%5E2%2F3x%5E2y%5E5\"$
\n" ); document.write( "Take the x term first:
\n" ); document.write( " $\"9x%5E2y%5E2%2F%283%282y%5E5%29%29\"$
\n" ); document.write( "Simplifying a little more gives you:
\n" ); document.write( " $\"3x%5E2y%5E2%2F%282y%5E5%29\"$
\n" ); document.write( "Now work on the y term. Notice that subtracting 5 from 2 gives you -3:
\n" ); document.write( " $\"3x%5E2y%5E%28-3%29\"$
\n" ); document.write( "This can be re-written as:
\n" ); document.write( " $\"highlight%283x%5E2%2Fy%5E3%29\"$
\n" ); document.write( "==============
\n" ); document.write( "Good Luck,
\n" ); document.write( "tutor_paul@yahoo.com
\n" ); document.write( " \n" ); document.write( "

\n" );