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Is there a "distributive property of division"??

Like as in this question:

(-3)2n+1 /(27*(-3)2n)  n is a positive whole number.

Can you do this:

((-3)2n+1 /27)*((-3)2n+1 /(-3)2n) ??????

THANK YOU

ISmellGood  Aug 26, 2017
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2+0 Answers

 #1
avatar+78618 
+2

(-3)2n+1 /(27*(-3)2n)

 

Note that we can write this as

 

(-3)2n+1 / (-3)2n   * ( 1 /27 )

 

And remember that we have the property that    am / an  = a ( m - n)

 

So   ...we have....

 

(-3) [ (2n + 1) - 2n ]  *  (1/27)  =

 

(-3)1  * (1/27)  =

 

(-3)  / 27  =

 

-1 / 9

 

 

cool cool cool

CPhill  Aug 26, 2017
 #2
avatar+5245 
+4

Also...

 

\(\frac{(-3)^{2n+1}}{27\,\cdot\,(-3)^{2n}}=\frac{(-3)^{2n+1}}{27}\,\cdot\,\frac{(-3)^{2n+1}}{(-3)^{2n}}\)

 

This is not true.

If you multiply the two fractions on the right side together, you will get   \(\frac{[ (-3)^{2n+1})]^2}{27\,\cdot\,(-3)^{2n}}\)     .

 

\(\frac{a}{bc}\,\neq\,\frac{a}{b}\,\cdot\,\frac{a}{c}\)

 

 

But..you can distribute division the same as you distribute multiplication, like this....

 

\(\frac{8 + 6 +10}{2}=\frac12(8+6+10)\,=\,(\frac12)(8)+(\frac12)(6)+(\frac12)(10)\,=\,4+3+5\,=\,12\)     smiley

hectictar  Aug 26, 2017
edited by hectictar  Aug 27, 2017

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