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TheYankee

  • one year ago

Higher roots with exponents?

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  1. TheYankee
    • one year ago
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    How do I simplify?

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  2. Nnesha
    • one year ago
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    factor x^{16} remember exponent rules \[\huge\rm x^m \times x^n = x^{m+n}\]

  3. Nnesha
    • one year ago
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    so you can write x^5 times x^5 times x^5 times x which is equal to ??

  4. Nnesha
    • one year ago
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    \[\huge\rm x^5 \times x^5 \times x^5 \times x= x^?\]

  5. Nnesha
    • one year ago
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    when we multiply same bases we should add their exponents :-) exponent rules \[\huge\rm x^m \times x^n = x^{m+n}\]

  6. TheYankee
    • one year ago
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    So, would it look like this?

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  7. Nnesha
    • one year ago
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    \[\huge\rm x^5 \times x^5 \times x^5 \times x= x^?\] you didn't answer my question :(

  8. TheYankee
    • one year ago
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    Wouldn't it be x^16? (I have such a problem with these >.< )

  9. Nnesha
    • one year ago
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    yes right

  10. Nnesha
    • one year ago
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    now factor them under the 5th root \[\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times x }\] just like square can cancelz out with square same idea here &that's why we have to make a pair of five exponent so we cancel them with 5th root solve that

  11. Nnesha
    • one year ago
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    you can convert root to exponent \[\huge\rm \sqrt[n]{x^m}= x^\frac{ m }{ n }\]

  12. TheYankee
    • one year ago
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    Oh! Alright! I didn't know that! (Please excuse my ineptitude... I'm a history person, lol....)

  13. TheYankee
    • one year ago
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    Huh! Would it be X^4, then?

  14. Nnesha
    • one year ago
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    convert 5th root to exponent

  15. TheYankee
    • one year ago
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    When you convert to an exponent, Each 5th root would result in one, correct? Making it just X instead of x rasied to a power.

  16. Nnesha
    • one year ago
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    yes right but x is same as x to the one power x^1

  17. TheYankee
    • one year ago
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    True. So because each x factor would result in x^1, I'm thinking the end result would be X^4.

  18. Nnesha
    • one year ago
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    \[\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times x }\] \[\huge\rm x^\frac{5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 1 }{ 5 }\] so it should be like this

  19. Nnesha
    • one year ago
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    \[\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times\color{reD}{ x} }\] red x doesn't have power so you cannot cancel 5th root. it should stay under the 5th rot \[\huge\rm x^\frac{5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 1 }{ 5 }\] so it should be like this

  20. TheYankee
    • one year ago
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    Omg! It makes sense now! Would it be x^3 5^(sqrt) x? (I'll model that answer in a second. Thanks for your patience ^^)

  21. Nnesha
    • one year ago
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    yes!

  22. Nnesha
    • one year ago
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    np :-)

  23. TheYankee
    • one year ago
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    To confirm, like this?

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  24. Nnesha
    • one year ago
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    yes

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