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DJJo

  • one year ago

Will give medal! How do I simplify the square root of the fourth root of 8 in exponential form?

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  1. DJJo
    • one year ago
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  2. anonymous
    • one year ago
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    \[\sqrt{\sqrt[4]{8}}=\sqrt{8^{\frac{ 1 }{ 4}}}=(8^{\frac{ 1 }{ 4 }})^{\frac{ 1 }{ 2 }}=8^{\frac{ 1 }{ 8}}=(2^{3})^{\frac{ 1 }{ 8 }}=2^{\frac{ 3 }{ 8 }}\]

  3. DJJo
    • one year ago
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    But I'm confused on how you got that @peachpi

  4. anonymous
    • one year ago
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    how is it confusing? things to power are multiplied with each other

  5. anonymous
    • one year ago
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    square root is the same as the exponent ½ fourth root is exponent ¼

  6. DJJo
    • one year ago
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    oh ok thank you @peachpi

  7. DJJo
    • one year ago
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    @peachpi Would you mind if I ask you another question?

  8. anonymous
    • one year ago
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    ok

  9. DJJo
    • one year ago
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    How would I simply this expression in exponential form?

  10. anonymous
    • one year ago
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    ok. this is the same type of problem. How would you write the numerator with an exponent?

  11. DJJo
    • one year ago
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    3 and 1/2

  12. anonymous
    • one year ago
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    exponents with bases being divided are subtracted eg. 3^(1/2) / 3^(1/4) = 3^ ((1/2) - (1/4))

  13. anonymous
    • one year ago
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    Yeah. Then √3 is also a part of the denominator so you can do this |dw:1434904015717:dw|

  14. DJJo
    • one year ago
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    So would the denominator be 3 and 1/8?

  15. anonymous
    • one year ago
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    no... 3 and 1/4

  16. anonymous
    • one year ago
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    It would be 3^(1/4) because 1/2 * 1/2 = 1/4

  17. anonymous
    • one year ago
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    |dw:1434904157793:dw|

  18. anonymous
    • one year ago
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    Now since the base is 3 on top and bottom you can subtract the exponents

  19. anonymous
    • one year ago
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    1/4 since as I have explained before... exponents, with bases same being multiplied, are added

  20. anonymous
    • one year ago
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    |dw:1434904205322:dw|

  21. DJJo
    • one year ago
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    So 3 and 1/4 would be the answer right?

  22. anonymous
    • one year ago
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    3 TO THE 1/4

  23. DJJo
    • one year ago
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    Yeah, that's what meant Thank you sooooo much @peachpi

  24. anonymous
    • one year ago
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    you're welcome

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