document.write( "Question 72786This question is from textbook Essential Algebra
\n" ); document.write( ": (-5w^2x^3y)(-wxz^3)(3vxy^2)(-4wz^3) Simplify. \n" ); document.write( "
Algebra.Com's Answer #52355 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Simplify:
\n" ); document.write( ".
\n" ); document.write( "\"%28-5w%5E2x%5E3y%29%2A%28-wxz%5E3%29%2A%283vxy%5E2%29%2A%28-4wz%5E3%29\"
\n" ); document.write( ".
\n" ); document.write( "Until you get a little more experience, let's do some things that will make it more difficult
\n" ); document.write( "to make a mistake.
\n" ); document.write( ".
\n" ); document.write( "In the term inside the second set of parentheses let's insert a multiplier of 1 so the term
\n" ); document.write( "becomes \"%28-1wxz%5E3%29\"
\n" ); document.write( ".
\n" ); document.write( "Let's go through all the terms and wherever we see a letter without an exponent, let's give
\n" ); document.write( "that letter an exponent of 1.
\n" ); document.write( ".
\n" ); document.write( "These two changes modify the expression so it now reads:
\n" ); document.write( ".
\n" ); document.write( "
\n" ); document.write( ".
\n" ); document.write( "One final thing ... let's identify all the variables to make sure we don't miss any. List them
\n" ); document.write( "in alphabetical order. The variables are: v, w, x, y, and z
\n" ); document.write( ".
\n" ); document.write( "Now let's attack the problem.
\n" ); document.write( ".
\n" ); document.write( "First multiply the numbers in front of all the terms. Make sure you keep them associated
\n" ); document.write( "with their correct sign. For this multiplication you should get:
\n" ); document.write( ".
\n" ); document.write( "\"%28-5%29%2A%28-1%29%2A%28%2B3%29%2A%28-4%29+=+-60\"
\n" ); document.write( ".
\n" ); document.write( "Now in order, go through all the variables, one at a time, and add their exponents.
\n" ); document.write( ".
\n" ); document.write( "v first. Adding the exponents of the letter v gives you an answer of \"v%5E1\" because the letter
\n" ); document.write( "v appears only once and its exponent is 1. Write it as just \"v\" instead of \"v%5E1\".
\n" ); document.write( ".
\n" ); document.write( "w second. Adding the exponents for w results in \"2%2B1%2B1+=+4\" so multiplication of
\n" ); document.write( "the w terms ends up as \"w%5E4\".
\n" ); document.write( ".
\n" ); document.write( "x next. Adding the exponents of x results in \"3+%2B+1+%2B+1=+5\" so the multiplication of
\n" ); document.write( "the x terms gives \"x%5E5\" as the answer.
\n" ); document.write( ".
\n" ); document.write( "y next. Adding the of y results in \"1%2B2+=+3\". So multiplication of the y terms gives
\n" ); document.write( "you an answer of \"y%5E3\".
\n" ); document.write( ".
\n" ); document.write( "Finally z terms ... add the exponents of z \"3%2B3=6\" indicating that the product of
\n" ); document.write( "the z terms results in \"z%5E6\"
\n" ); document.write( ".
\n" ); document.write( "As a check add up all the exponents of our answers. \"1%2B4%2B5%2B3%2B6+=+19\". Then go back to
\n" ); document.write( "the original problem and add up all the exponents that appear in the problem. \"2%2B3%2B1%2B1%2B1%2B3%2B1%2B1%2B2%2B1%2B3+=+19\"
\n" ); document.write( "The count agrees so we probably did not make an error.
\n" ); document.write( ".
\n" ); document.write( "Now multiply all our answers together to get:
\n" ); document.write( ".
\n" ); document.write( "\"%28-60%29%2Avw%5E4x%5E5y%5E3z%5E6\"
\n" ); document.write( ".
\n" ); document.write( "That's the answer.
\n" ); document.write( ".
\n" ); document.write( "Hope this helps you to understand the problem. Once you get used to it, you'll be able to
\n" ); document.write( "eliminate some of the steps such as inserting exponents of 1 to make sure you don't miscount.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );