Question:

How do you solve this (-2)^-3?

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How do you solve this (-2)^-3?

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  1. -2ֿ³ = 0.125


  2. So couple of rules: any neg exponent is the reciprocal (basically the number you times it by to get one so put it under one)

    ie:

    the recipocal of 2 is 1/2      

               2 x 1/2 = 1



    the recipocal of 3 is 1/3        

               3 x 1/3 = 1

    neg numbers alternate positive to neg when they are multiplied out ie:

    -2 x -2 = 4     and -2 x -2 x -2 = -8

    so       (factoring out)       -2 x -2 x -2 = -8    

    Then give it a reciprocal     (-1/8)

    This is your answer it is quite simple when you learn the rules

    (-1/8)

  3. A number raised to a negative integer exponent is defined as one over the number raised to the positive integer exponent.In other words,

    x^(-a) = 1/(x^a)

    In this case, x = -2 and a = 3.

    (-2)^(-3) = 1 / ((-2)^3) = 1 / (-2 * -2 * -2) = 1 / (-8)

    So, the answer is -1/8

  4. The rules to know for this problem are:

    1) a nonzero number to the −1 power produces its reciprocal.

    2) a^n = a x a x a x a .... n times

    Use rule 1 to evaluate a^-n

    a^-n = (a^n)^-1 = 1/a^n

    (-2)¯³ = 1/(-2)³

    Now use rule 2 to evaluate (a)^n

    1/(-2)³ = (1/-2) x (1/-2) x (1/-2) = (1/4) x (1/-2) = 1/-8 = -1/8

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