SOLUTION: I have to simplify the polynomial and i am really confused. This problem is so different then the examples given in the text... {{{3x(x^5)^2}}} divided by {{{6x ^3(x^2)^4 }}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have to simplify the polynomial and i am really confused. This problem is so different then the examples given in the text... {{{3x(x^5)^2}}} divided by {{{6x ^3(x^2)^4 }}}       Log On


   

Question 127400: I have to simplify the polynomial and i am really confused. This problem is so different then the examples given in the text...
3x%28x%5E5%29%5E2 divided by 6x+%5E3%28x%5E2%29%5E4+

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
3x%28x%5E5%29%5E2 divided by 6x+%5E3%28x%5E2%29%5E4+
.
or
.
%283x%28x%5E5%29%5E2%29%2F%286x+%5E3%28x%5E2%29%5E4+%29
.
When you square x%5E5 you can think of this in two ways. You multiply the exponent 2
times the exponent 5 to get x%5E10 or you multiply x%5E5 times itself to get:
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x%5E5+%2Ax%5E5+=+x%5E%285%2B5%29+=+x%5E10
.
In either case, you substitute x%5E10 for %28x%5E5%29%5E2 in the numerator and the problem
then becomes:
.
%283x%28x%5E10%29%29%2F%286x+%5E3%28x%5E2%29%5E4%29
.
Now let's work on the term %28x%5E2%29%5E4 in the denominator. If you multiply the two exponents
you get %28x%5E2%29%5E4+=+x%5E8 which is also what you get if you multiply x%5E2 by itself
4 times. Substituting this into the denominator makes the problem become:
.
%283x%28x%5E10%29%29%2F%286x+%5E3%28x%5E8%29%29
.
Back to the numerator. If you multiply 3x times x%5E10 you add the exponents of
the x terms and you get 3x%5E11 for the numerator.
.
Then to the denominator. In multiplying x%5E3 by x%5E8 you get x%5E11 by
adding the exponents. Then with the factor 6 the denominator becomes 6x%5E11. With
these reductions of the numerator and the denominator the problem then is reduced to:
.
%283x%5E11%29%2F%286x%5E11%29
.
Dividing the x%5E11 of the numerator by the x%5E11 of the denominator results in
.
x%5E11%2Fx%5E11+=+x%5E%2811-11%29+=+x%5E0+=+1
.
[or you could just view this as canceling the x%5E11 of the numerator with the counterpart
x%5E11 in the denominator.] This reduction leaves you with:
.
3%2F6+=+1%2F2
.
And so, the answer to this problem is that it all simplifies down to 1%2F2
.
Hope this helps you to understand the problem and one way you might solve it.
.