Can someone explain why this happens? (Dividing variables with exponents)Alright, so let's say I have x − 6 − x − 4 The answer is 1 x 2 , but why isn't it 1 − x 2 ??

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Can someone explain why this happens? (Dividing variables with exponents)Alright, so let&#039;s say I have            x              −        6                    −              x                  −          4                    The answer is             1              x        2            , but why isn&#039;t it             1              −                  x          2                    ??

sleuteleni7 · Accepted Answer

Let&#039;s think about what negative exponents really mean. Consider the following list      2    3    =  8      2    2    =  4      2    1    =  2Notice that every time we decrease an exponent, we divide by 2. Continuing this list, we have that      2    3    =  8      2    2    =  4      2    1    =  2      2    0    =  1      2          −      1        =  1      /    2      2          −      2        =  1      /    4Rather interesting, we see a pattern:       2          −      n        =      1          2      n      . Therefore there is no reason for a negative sign on the quantity itself, since we&#039;re successively dividing by positive numbers.

Emmy Knox · Accepted Answer

It might help you see what&#039;s going on if you write them as two story fractions:            x              −        6                    −              x                  −          4                      =            (                        1                      x            6                              )              (      −                        1                      x            4                              )        =                                          1                          x              6                                ×          −                                    x              4                        1                          ⏟                                      by the reciprocal rule                      =  −      1          x      2        =      1          −              x        2            So you are correct, and the &quot;answer&quot; is wrong.]

Can someone explain why this happens? (Dividing variables with exponents) Alright, so let's say I

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