What is the reciprocal of ( − 1 / 2 ) k The answer is meant to be 2 − k as if you flip something upside down the power becomes negative. However, I am not sure what happens to the negative in front of the fraction.

Question

What is the reciprocal of   (  −  1      /    2      )    k  The answer is meant to be       2          −      k       as if you flip something upside down the power becomes negative. However, I am not sure what happens to the negative in front of the fraction.

Austin Solis · Accepted Answer

The reciprocal of x is simply       1    x  . So the reciprocal of   (  −            1      2            )    k   is       1          (      −                        1          2                            )        k            .You may also recall from the exponentiation laws that    (      1    x        )    y    =      x          −      y      , and that the repciprocal of       x    y   is       1          x      y        =      x          −      y      . This allows us to rewrite   (  −            1      2            )    k   as   (  −  2      )          −      k      , and then the reciprocal of this is    (  −  2      )    k  . If k is even, this simplifies to       2    k  ; if k is odd, it becomes   −      2    k

Quintacj · Accepted Answer

Condensed form of Hagen&#039;s answer:       1          (      −              1        2                    )        k              =      1                  (        −        1                  )          k                            2        k              =            2      k              (      −      1              )        k              =      {                                        2            k                                                if                           k                         is even,                                                −                      2            k                                                if                           k                         is odd.

What is the reciprocal of ( − 1 <mrow class="MJX-TeXAtom-ORD"> /

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