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11 December, 15:23

Evaluate 1 / 2^-2x^-3y^5 for x=2 and y=-4

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Answers (1)
  1. 11 December, 15:46
    0
    -512

    Step-by-step explanation:

    Evaluate y^5 / (x^3/2^2) where x = 2 and y = - 4:

    (y^5) / (2^ (-2) x^3) = (-4) ^5/2^ (-2) * 1/2^3

    2^3 = 2*2^2:

    (-4) ^5/2^ (-2) 1 / (2*2^2)

    2^2 = 4:

    (-4) ^5 / ((2*4) / 2^2)

    2*4 = 8:

    (-4) ^5 / (8/2^2)

    2^ (-2) = 1/4:

    ((-4) ^5/8) / (1/4)

    (-4) ^5 = (-1) ^5*4^5 = - 4^5:

    ((-4^5) / 8) / (1/4)

    4^5 = 4*4^4 = 4 (4^2) ^2:

    ((-4 (4^2) ^2) / 8) / (1/4)

    4^2 = 16:

    ((-4*16^2) / 8) / (1/4)

    | 1 | 6

    * | 1 | 6

    | 9 | 6

    1 | 6 | 0

    2 | 5 | 6:

    ((-4*256) / 8) / (1/4)

    4*256 = 1024:

    ((-1024) / 8) / (1/4)

    Multiply the numerator by the reciprocal of the denominator, ((-1024) / 8) / (1/4) = (-1024) / 8*4:

    (-1024*4) / 8

    (-1024) / 8 = (8 (-128)) / 8 = - 128:

    -128*4

    -128*4 = - 512:

    Answer: - 512
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