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Math Help - Need Help Exponents

  1. #1
    TH1
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    Need Help Exponents

    I need to write these in exponential form and use exponent laws to simplify and evaluate any help would be appreciated

    <br />
\sqrt{1000}    X    \sqrt[3]{1000} /  \sqrt[6]{1000}<br />
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  2. #2
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    Hello, TH1;98010!

    Simplify and evaluate: . \frac{<br />
\sqrt{1000}\cdot\sqrt[3]{1000}}{\sqrt[6]{1000}}
    Write in exponential form:

    . . \frac{(10^3)^{\frac{1}{2}}\cdot(10^3)^{\frac{1}{3}  }}{(10^3)^{\frac{1}{6}}} \;=\;\frac{10^{\frac{3}{2}}\cdot10^1}{10^{\frac{1}  {2}}} \;= \;10^{(\frac{3}{2}+1-\frac{1}{2})} \;=\;10^2\;=\;100

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  3. #3
    TH1
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    Thanks for the help I have a couple more since I couldnt work out the code


    <br />
\left( \sqrt{64} \right)^2  /   \sqrt[3]{64}<br />

    <br />
4+4^1 / 4-4{^1}<br />
    For the second question the exponents are negative both of them

    <br />
\sqrt{4^3}(\sqrt[5]{4^4}) /  \sqrt{2^10}<br />
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  4. #4
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    Hello,TH1!

    \frac{\left( \sqrt{64} \right)^2}{\sqrt[3]{64}}

    We have: . \frac{(64^{\frac{1}{2}})^2}{64^{\frac{1}{3}}} \;=\;\frac{64^1}{64^{\frac{1}{3}}} \;=\;64^{(1-\frac{1}{3})} \;=\;64^{\frac{2}{3}}\;=\;(\sqrt[3]{64})^2 \;=\;4^2\;=\;16



    \frac{4+4^{-1}}{4-4^{-1}}
    Multiply by \frac{4}{4}\!:\;\;\frac{4}{4}\cdot\frac{4 + 4^{-1}}{4 - 4^{-1}} \;=\;\frac{16+1}{16-1} \;=\; \frac{17}{15}


    \frac{\sqrt{4^3}\cdot\sqrt[5]{4^4}}{\sqrt{2^{10}}}
    Change all the bases to 2s.

    \frac{\sqrt{(2^2)^3}\cdot\sqrt[5]{(2^2)^4} }{\sqrt{2^{10}}} \;=\;\frac{(2^6)^{\frac{1}{2}} (2^8)^{\frac{1}{5}}} {(2^{10})^{\frac{1}{2}}}  \;=\;\frac{2^3\cdot2^{\frac{8}{5}}}{2^5} \;=\;2^{(3+\frac{8}{5}-5)} \;=\;2^{-\frac{2}{5}}

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