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anonymous

  • one year ago

\[\frac{(x ^{-5}x ^{4})^{4} }{ (x ^{4}x ^{-6})^{-5}}\]

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  1. anonymous
    • one year ago
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    How do i do this...Yes it may be simple but for some reason i can't figure it out.

  2. TheSmartOne
    • one year ago
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    Hint: First use this formula \(\sf(a^b)^c = a^{b\times c}\) Then use this one \(\sf\Large\frac{a^b}{a^c}=a^{b-c}\)

  3. anonymous
    • one year ago
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    I know that

  4. TheSmartOne
    • one year ago
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    also these formulas: \(\sf a^b\times a^c = a^{b+c}\) \(\sf\Large {a^{-b}}=\frac{1}{a^b}\)

  5. anonymous
    • one year ago
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    yes i understand that...i just can't seem to get the correct answer to this...

  6. phi
    • one year ago
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    can you simplify \[ x ^{-5}x ^{4} \]? (add the exponents)

  7. anonymous
    • one year ago
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    x^-1

  8. phi
    • one year ago
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    yes now we have up top \[ (x^{-1})^4 \] now use the rule multiply exponents to simplify that

  9. anonymous
    • one year ago
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    X^-4

  10. phi
    • one year ago
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    now let's do the bottom. first \[ (x ^{4}x ^{-6}) \]

  11. anonymous
    • one year ago
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    x^-2

  12. phi
    • one year ago
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    now (x^-2)^-5

  13. anonymous
    • one year ago
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    x^10

  14. phi
    • one year ago
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    so we have \[ \frac{x^{-4}}{x^{10} }\]

  15. anonymous
    • one year ago
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    so 1/ x^14

  16. phi
    • one year ago
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    you can do that two ways: "flip" x^-4 and put it in the bottom but with x^4 then combine x^4*x^10 (in the bottom) or do -4 - 10 (subtract the exponents because we divide)

  17. phi
    • one year ago
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    yes 1/x^14 this can also be written x^(-14)

  18. anonymous
    • one year ago
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    ok thank you!

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