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Math Help - Ticky expression

  1. #1
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    Ticky expression

    I'm trying to solve this problem step by step with positive exponents. I still can't seem to find the correct answer but here is the problem
    [(2x^2)(z^-5))/(3z^4)]^-5
    Divided By
    [((3x^4)(z^9))/(2x^-6)]^3
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  2. #2
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    Quote Originally Posted by sgonzalez90 View Post
    I'm trying to solve this problem step by step with positive exponents. I still can't seem to find the correct answer but here is the problem
    [(2x^2)(z^-5))/(3z^4)]^-5
    Divided By
    [((3x^4)(z^9))/(2x^-6)]^3
    You mean simplify this?
    \left(\frac{2x^2 z^{-5}}{3z^4}\right)^{-5} \div \left(\frac{3x^4 z^9}{2x^{-6}}\right)^{3}

    I'd take the reciprocal of the first fraction and change the outer exponent to a positive one:
    \left(\frac{3z^4}{2x^2 z^{-5}}\right)^5 \div \left(\frac{3x^4 z^9}{2x^{-6}}\right)^{3}

    Then I'd multiply the reciprocal of the second fraction (note that the outermost exponent does not change):
    \left(\frac{3z^4}{2x^2 z^{-5}}\right)^5 \times \left(\frac{2x^{-6}}{3x^4 z^9}\right)^3

    Move the remaining negative exponents:
    \left(\frac{3z^4 z^5}{2x^2}\right)^5 \times \left(\frac{2}{3x^4 z^9 x^6}\right)^3

    \left(\frac{3z^9}{2x^2}\right)^5 \times \left(\frac{2}{3x^{10} z^9}\right)^3

    Apply the Power-of-a-Power property:
    \frac{3^5 z^{45}}{2^5 x^{10}} \times \frac{2^3}{3^3 x^{30} z^{27}}

    Multiply and simplify:
    \frac{2^3 3^5 z^{45}}{2^5 3^3 x^{40} z^{27}}

    \frac{3^2 z^{18}}{2^2 x^{40}}

    \frac{9z^{18}}{4x^{40}}


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  3. #3
    MHF Contributor Amer's Avatar
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    I am always late
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  4. #4
    MHF Contributor Amer's Avatar
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    Thanks yeongil
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