advanced algebra

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Q. x^-4/5=16 What is x Q. Suppose 0<a<1. Arrange the following from smallest to largest z^-a,z^a,z^1/a,z^-1/8.

  • advanced algebra -

    x^-4/5=16
    x^4/5=1/16
    (x^4/5)^(5/4) = (1/16)^(5/4)
    x = 1/32

    your second is ambiguous

    the terms are
    (1/z)^a , z^a, z^(1/a) and (1/z)^(1/8)

    it depends on the value of z
    e.g. if z = 1, all terms have the same value
    if z>1
    investigate:
    let z = 4, a = .2
    (1/4)^.2 = .758
    4^.2 = 1.32
    4^(1/.2) = 1024
    (1/4)^(1/8) = .84

    arrange the terms according to the answers

    now what about 0< z < 1
    repeat my method and decide for that case

    if z < 0 , that is if z is negative you will run into all kinds of undefined situations when you take roots.

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