document.write( "Question 176298: Simplify [√32x^5y^2] / [√2x^3y^3] Thank you. \n" ); document.write( "
Algebra.Com's Answer #131394 by EMStelley(208)\"\" \"About 
You can put this solution on YOUR website!
First of all, I have to assume this is what you mean:
\n" ); document.write( "\"%28sqrt%2832%29x%5E5y%5E2%29%2F%28sqrt%282%29x%5E3y%5E3%29\"
\n" ); document.write( "First, let's deal with sqrt(32). Note that since 32=16*2, we can write it as
\n" ); document.write( "\"sqrt%2832%29=sqrt%2816%2A2%29=sqrt%2816%29sqrt%282%29=4sqrt%282%29\"
\n" ); document.write( "So we have
\n" ); document.write( "\"%284sqrt%282%29x%5E5y%5E2%29%2F%28sqrt%282%29x%5E3y%5E3%29\"
\n" ); document.write( "Now, the sqrt(2) will cancel out, leaving:
\n" ); document.write( "\"%284x%5E5y%5E2%29%2F%28x%5E3y%5E3%29\"
\n" ); document.write( "Now, there is x^5 on top and x^3 on bottom. You can look at this two ways: if you were to write them out, you'd have xxxxx/xxx. Three of the x's would cancel, leaving two on top, or x^2. The rule is, when you have division, you subtract the exponents. So x^5/x^3=x^(5-3)=x^2. Similarly, with the y's we are left with one on the bottom. So simplified we have:
\n" ); document.write( "\"%284x%5E2%29%2Fy\" \n" ); document.write( "
\n" );