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

Question

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

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Lydia 2 weeks 2021-09-13T14:10:38+00:00 1 Answer 0

Answers ( )

    0
    2021-09-13T14:12:32+00:00

    Answer:

    -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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