SOLUTION: Please help me with this: [(6x^5y^3z)*3x^2]/(2xy^2z^5)

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Question 177651: Please help me with this:
[(6x^5y^3z)*3x^2]/(2xy^2z^5)

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is:
%28%286%2Ax%5E5%2Ay%5E3%2Az%29%2A3%2Ax%5E2%29%2F%282%2Ax%2Ay%5E2%2Az%5E5%29
if you remove the parentheses from the numerator, this becomes:
%286%2Ax%5E5%2Ay%5E3%2Az%2A3%2Ax%5E2%29%2F%282%2Ax%2Ay%5E2%2Az%5E5%29
since a*b is the same as b*a, you can move the variables around until you get similar variables together which makes your equation the same as:
%286%2A3%2Ax%5E5%2Ax%5E2%2Ay%5E3%2Az%29%2F%282%2Ax%2Ay%5E2%2Az%5E5%29
since x%5E5+%2A+x%5E2+=+x%5E%285%2B2%29+=+x%5E7, your equation becomes:
%286%2A3%2Ax%5E7%2Ay%5E3%2Az%29%2F%282%2Ax%2Ay%5E2%2Az%5E5%29
since x%5E7+%2F+x+=+x%5E7+%2F+x%5E1+=+x%5E%287-1%29+=+x%5E6, your equation becomes:
%286%2A3%2Ax%5E6%2Ay%5E3%2Az%29%2F%282%2Ay%5E2%2Az%5E5%29
since y%5E3+%2F+y%5E2+=+y%5E%283-2%29+=+y%5E1+=+y, your equation becomes:
%286%2A3%2Ax%5E6%2Ay%2Az%29%2F%282%2Az%5E5%29
since z+%2F+z%5E5+=+z%5E1+%2F+z%5E5+=+z%5E%281-5%29+=+z%5E%28-4%29+=+1%2Fz%5E4, your equation becomes:
%286%2A3%2Ax%5E6%2Ay%29%2F%282%2Az%5E4%29
since %286%2A3%29%2F2+=+3%2A3+=+9, your equation becomes:
%289%2Ax%5E6%2Ay%29%2F%28z%5E4%29
since you can't simplify any further, this will be your final equation.
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to prove your answer is correct, substitute values for x, y, and z in your original equation and in your final equation to see that the answer comes out the same.
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let:
x = 2
y = 3
z = 4
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your final equation is:
%289%2Ax%5E6%2Ay%29%2F%28z%5E4%29
substituting, we get:
%289%2A2%5E6%2A3%29%2F%284%5E4%29
which becomes:
%289%2A64%2A3%29%2F%28256%29
which becomes:
%281728%29%2F%28256%29
which becomes:
6.75
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your original equation is:
%286%2Ax%5E5%2Ay%5E3%2Az%2A3%2Ax%5E2%29%2F%282%2Ax%2Ay%5E2%2Az%5E5%29 after removing the parentheses.
substituting, we get:
%286%2A2%5E5%2A3%5E3%2A4%2A3%2A2%5E2%29%2F%282%2A2%2A3%5E2%2A4%5E5%29
which becomes:
%286%2A32%2A27%2A4%2A3%2A4%29%2F%282%2A2%2A9%2A1024%29
which becomes:
%28248832%29%2F%2836864%29
which becomes:
6.75
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since the original equation = 6.75 and the final equation = 6.75, then the original equation equals the final equation and we are good.
---
your answer is:
%28%286%2Ax%5E5%2Ay%5E3%2Az%29%2A3%2Ax%5E2%29%2F%282%2Ax%2Ay%5E2%2Az%5E5%29 = %289%2Ax%5E6%2Ay%29%2F%28z%5E4%29