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Math Help - Evaluate and find exact values

  1. #1
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    Evaluate and find exact values

    Find the Exact Values
    125^1/3 - 10^0(64)^2/3

    Here is what i done for the first one

    3root125 - 10 1/3root(64^2)

    5- 160
    = -155

    The answer from the key is -11. ^^;;; stuck..

    Evaluate a=1 b=2 c=3

    1. (a^-2 b^-4) (a^2 b^-5)



    2. a^-1 b^3 c^-2/abc

    For the evaluates i turned all the negative exponents into positive fractions. After that i multipled/divde all the numbers and got some werid numbers..

    answer key for #1 is -1/512 #2 4/27

    Also when you getting rid of the negative exponent for e.g:

    -2^-1/2 becomes 1/ 2or -2 ^ 1/2 does the base stays negative or it changes into positive with the exponent?

    Thank You
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  2. #2
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    Quote Originally Posted by hovermet View Post
    Find the Exact Values
    125^1/3 - 10^0(64)^2/3

    Here is what i done for the first one

    3root125 - 10 1/3root(64^2)

    5- 160
    = -155

    The answer from the key is -11. ^^;;; stuck..

    Evaluate a=1 b=2 c=3

    1. (a^-2 b^-4) (a^2 b^-5)



    2. a^-1 b^3 c^-2/abc

    For the evaluates i turned all the negative exponents into positive fractions. After that i multipled/divde all the numbers and got some werid numbers..

    answer key for #1 is -1/512 #2 4/27

    Also when you getting rid of the negative exponent for e.g:

    -2^-1/2 becomes 1/ 2or -2 ^ 1/2 does the base stays negative or it changes into positive with the exponent?

    Thank You
    125^(1/3) = 3rd root of 125 = 5 You had that bit correct!
    10^0 = 1 ...remember a^0 = 1 as long as a doesn't equal 1
    64^(2/3) ... two ways to do this:
    1) square 64 then take cube root (not the best way because the numbers are too big to do in your head) OR
    2) Take the cube root of 64 (which is 4) and then square it (to get 16)
    Son the answer is 5 - 1x16 = -11 !!
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  3. #3
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    Hello, hovermet!

    Find the Exact Values: 125^(1/3) - (10^0)(64)^(2/3)

    Here is what i did for the first one

    3root(125) - 10 3root(64^2)
    . . . . . . . . . . {\color{blue}\uparrow}
    . . . . . . . {\color{blue}\text{No, }10^0 = 1}

    Evaluate for a=1,\: b=\text{-}2,\: c=3

    1.\;\;\left(a^{-2} b^{-4}\right)\left(a^2 b^{-5}\right)
    Simplify first: . \left(a^{-2}b^{-4}\right)\left(a^2b^{-5}\right) \:=\:b^{-9} \:=\:\frac{1}{b^9}

    Evaluate: . \frac{1}{b^9} \;=\;\frac{1}{(\text{-}2)^9} \;=\;\frac{1}{\text{-}512} \;=\;-\frac{1}{512}



    2.\;\;\frac{a^{-1} b^3 c^{-2}}{abc}
    Simplify: . \frac{a^{-1}b^3c^{-2}}{abc} \;=\;\frac{b^2}{a^2c^3}

    Evaluate: . \frac{(-2)^4} {(1)^2(3)^3} \;=\;\frac{16}{1\cdot27} \;=\;\frac{16}{27}

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