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