SOLUTION: (-5w^2x^3y)(-wxz^3)(3vxy^2)(-4wz^3) Simplify.

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
.
%28-5w%5E2x%5E3y%29%2A%28-wxz%5E3%29%2A%283vxy%5E2%29%2A%28-4wz%5E3%29
.
Until you get a little more experience, let's do some things that will make it more difficult
to make a mistake.
.
In the term inside the second set of parentheses let's insert a multiplier of 1 so the term
becomes %28-1wxz%5E3%29
.
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.
.
These two changes modify the expression so it now reads:
.

.
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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%28-5%29%2A%28-1%29%2A%28%2B3%29%2A%28-4%29+=+-60
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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 v%5E1 because the letter
v appears only once and its exponent is 1. Write it as just v instead of v%5E1.
.
w second. Adding the exponents for w results in 2%2B1%2B1+=+4 so multiplication of
the w terms ends up as w%5E4.
.
x next. Adding the exponents of x results in 3+%2B+1+%2B+1=+5 so the multiplication of
the x terms gives x%5E5 as the answer.
.
y next. Adding the of y results in 1%2B2+=+3. So multiplication of the y terms gives
you an answer of y%5E3.
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Finally z terms ... add the exponents of z 3%2B3=6 indicating that the product of
the z terms results in z%5E6
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As a check add up all the exponents of our answers. 1%2B4%2B5%2B3%2B6+=+19. Then go back to
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
The count agrees so we probably did not make an error.
.
Now multiply all our answers together to get:
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%28-60%29%2Avw%5E4x%5E5y%5E3z%5E6
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That's the answer.
.
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.