Question 72786
Simplify:
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{{{(-5w^2x^3y)*(-wxz^3)*(3vxy^2)*(-4wz^3)}}}
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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 {{{(-1wxz^3)}}}
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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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{{{(-5w^2x^3y^1)*(-1w^1x^1z^3)*(3v^1x^1y^2)*(-4w^1z^3)}}}
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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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{{{(-5)*(-1)*(+3)*(-4) = -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^1}}} because the letter
v appears only once and its exponent is 1. Write it as just {{{v}}} instead of {{{v^1}}}. 
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w second. Adding the exponents for w results in {{{2+1+1 = 4}}} so multiplication of
the w terms ends up as {{{w^4}}}.
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x next. Adding the exponents of x results in {{{3 + 1 + 1= 5}}} so the multiplication of
the x terms gives {{{x^5}}} as the answer.
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y next.  Adding the of y results in {{{1+2 = 3}}}. So multiplication of the y terms gives
you an answer of {{{y^3}}}.
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Finally z terms ... add the exponents of z {{{3+3=6}}} indicating that the product of
the z terms results in {{{z^6}}}
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As a check add up all the exponents of our answers. {{{1+4+5+3+6 = 19}}}. Then go back to
the original problem and add up all the exponents that appear in the problem. {{{2+3+1+1+1+3+1+1+2+1+3 = 19}}}
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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{{{(-60)*vw^4x^5y^3z^6}}}
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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.