Fraction with negative exponent fraction.Q: ( 27 a 6 b − 3 c − 2 ) − 2 / 3 A: b 2 9 a 4 c 4 / 3 How in the world are they getting that?

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Fraction with negative exponent fraction.Q:            (                        27                      a            6                                b                          −              3                                                c                      −            2                              )              −      2              /            3      A:            b      2              9              a        4                    c                  4                      /                    3                    How in the world are they getting that?

Aaron Everett · Accepted Answer

For one thing,            27              a        6                    b                  −          3                            c              −        2            is equal to                    3        3                    a        6                    c        2                    b      3        .Putting that to the power of    −      2    3   is the same as first putting it to the power of -1, then to the power of 2, then to the power of       1    3   , so            (                        27                      a            6                                b                          −              3                                                c                      −            2                              )              −              2        3              =            (                        (                                    (                                                                    3                    3                                                        a                    6                                                        c                    2                                                                    b                  3                                            )                                      −              1                                )                2            )                      1        3              .Now, simply collaps the parentheses from the inside out.

Brunton39 · Accepted Answer

(                        27                      a            6                                b                          −              3                                                c                      −            2                              )              −      2              /            3        =            (              27                  −          2                      /                    3                    )      (              a                  (          6          )          (          −          2                      /                    3          )                    )      (              b                  (          −          3          )          (          −          2                      /                    3          )                    )              c              (        −        2        )        (        −        2                  /                3        )              =            b      2                      27                  2                      /                    3                            a                  12                      /                    3                            c                  4                      /                    3                      =            b      2              (              27                  1                      /                    3                            )        2                    a        4                    c                  4                      /                    3                      =            b      2              (      3              )        2                    a        4                    c                  4                      /                    3                      =            b      2              9              a        4                    c                  4                      /                    3

Fraction with negative exponent fraction. Q: ( 27

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