Applied Calculus

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2^(3/4)*4^(-3/2)

  • Applied Calculus -

    I know how to solve it to get .21, but I need to write it using positive exponents only. I know this isn't technically Calculus, but it is what we are reviewing currently. I am a bit rusty with this one, can't quite remember how to do it. I am trying some different things, but would greatly appreciate an explanation. Thank you!

  • Applied Calculus -

    since 4=2^2,
    4^(-3/2) = (2^2)^(-3/2) = 2^-3

    2^(3/4) * 2^-3 = 2^(3/4-3) = 2^(-9/4)
    = 1/(4*2^(1/4)) = 0.21

    Or, if you want positive exponents from the get-go,

    4^(-3/2) = 1/4^(3/2)

    2^(3/4) / 4^(3/2)
    = 2^(3/4) / 2^3
    = 1 / 2^(9/4)
    = 0.21

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