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# Simplify

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SImplify  $$\dfrac{7x^{2014}}{4x^{2013}}\cdot{\dfrac{2x^{2012}}{2x^{2007}}}\cdot\dfrac{27x^{2006}}{x^{2002}}\cdot\dfrac{6x^{2008}}{8x^{2010}}.$$

May 5, 2022

#1
+118574
+2

I will start you off.

$$\dfrac{7x^{2014}}{4x^{2013}}\cdot{\dfrac{2x^{2012}}{2x^{2007}}}\cdot\dfrac{27x^{2006}}{x^{2002}}\cdot\dfrac{6x^{2008}}{8x^{2010}}$$

$$=\dfrac{7x^{2014-2013}}{4^{2013}}\cdot{\dfrac{2x^{2012}}{2x^{2007}}}\cdot\dfrac{27x^{2006}}{x^{2002}}\cdot\dfrac{6x^{2008}}{8x^{2010}}.\\ ~\\=\dfrac{7x^{1}}{2^{2*2013}}\cdot{\dfrac{2x^{2012}}{2x^{2007}}}\cdot\dfrac{27x^{2006}}{x^{2002}}\cdot\dfrac{6x^{2008}}{8x^{2010}}$$

Now it is your turn.

May 6, 2022
edited by Melody  May 6, 2022
#2
+125697
+1

Here's another way

Multiply all the constants  on top  and  bottom  =   7 * 2 * 27 * 6              42 *27          21 * 27

__________  =         ______  =    _______  =

4 * 2 * 1 * 8                 4 * 8              2 * 8

567 / 16

Now look at  the  rest

The first  fraction   gives us   x^(2014 -2013)  =  x^1

The second fraction gives us x^(2012 - 2007) = x^5

The third fraction gives us    x^(2006 - 2002)  = x^4

And the last one  gives us     x^(2008 -2010) =x^(-2)

So

x * x^5 * x^4 * x^(-2)  =  x^( 1 + 5 + 4 - 2)  =  x^8

So...our  answer is  just     (567 / 16) x^8

May 6, 2022
edited by CPhill  May 6, 2022