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Math Help - Perform the indicated operations and simplify equation completely.

  1. #1
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    Exclamation Perform the indicated operations and simplify equation completely.

    I have a couple of problems I haven't been able to work out correctly...

    1.
    I am confused because of the negative exponents in this problem:

    t^-6 (2t)^3
    ------------
    t^3


    2.
    (x^4 + 4x^2 - 5x + 3) - (2x - 5)^2


    If anyone could help me with these asap, that would be great! Thanks.
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  2. #2
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    Quote Originally Posted by rckstr4lfe View Post
    I have a couple of problems I haven't been able to work out correctly...

    1.
    I am confused because of the negative exponents in this problem:

    t^-6 (2t)^3
    ------------
    t^3


    2.
    (x^4 + 4x^2 - 5x + 3) - (2x - 5)^2


    If anyone could help me with these asap, that would be great! Thanks.
    to #1:

    Use the laws of powers:

    \dfrac{t^{-6} \cdot (2t)^3}{t^3} = 8t^{-6+3-3}=8t^{-6} = \dfrac8{t^{6}}=\left(\dfrac2{t^2}\right)^3

    to #2:
    Expand the brackets and collect like terms:

    (x^4 + 4x^2 - 5x + 3) - (2x - 5)^2 = x^4+4x^2-5x+3-4x^2+20x-25 = x^4+15x-22
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