Question 127400
Given:
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{{{3x(x^5)^2}}} divided by {{{6x ^3(x^2)^4 }}}
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or
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{{{(3x(x^5)^2)/(6x ^3(x^2)^4 )}}}
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When you square {{{x^5}}} you can think of this in two ways. You multiply the exponent 2 
times the exponent 5 to get {{{x^10}}} or you multiply {{{x^5}}} times itself to get:
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{{{x^5 *x^5 = x^(5+5) = x^10}}}
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In either case, you substitute {{{x^10}}} for {{{(x^5)^2}}} in the numerator and the problem
then becomes:
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{{{(3x(x^10))/(6x ^3(x^2)^4)}}}
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Now let's work on the term {{{(x^2)^4}}} in the denominator. If you multiply the two exponents
you get {{{(x^2)^4 = x^8}}} which is also what you get if you multiply {{{x^2}}} by itself
4 times. Substituting this into the denominator makes the problem become:
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{{{(3x(x^10))/(6x ^3(x^8))}}}
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Back to the numerator. If you multiply {{{3x}}} times {{{x^10}}} you add the exponents of
the x terms and you get {{{3x^11}}} for the numerator.
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Then to the denominator. In multiplying {{{x^3}}} by {{{x^8}}} you get {{{x^11}}} by 
adding the exponents. Then with the factor 6 the denominator becomes {{{6x^11}}}. With
these reductions of the numerator and the denominator the problem then is reduced to:
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{{{(3x^11)/(6x^11)}}}
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Dividing the {{{x^11}}} of the numerator by the {{{x^11}}} of the denominator results in
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{{{x^11/x^11 = x^(11-11) = x^0 = 1}}}
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[or you could just view this as canceling the {{{x^11}}} of the numerator with the counterpart
{{{x^11}}} in the denominator.] This reduction leaves you with:
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{{{3/6 = 1/2}}}
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And so, the answer to this problem is that it all simplifies down to {{{1/2}}}
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Hope this helps you to understand the problem and one way you might solve it.
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