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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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How do i do this...Yes it may be simple but for some reason i can't figure it out.
Hint: First use this formula \(\sf(a^b)^c = a^{b\times c}\) Then use this one \(\sf\Large\frac{a^b}{a^c}=a^{b-c}\)
I know that

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also these formulas: \(\sf a^b\times a^c = a^{b+c}\) \(\sf\Large {a^{-b}}=\frac{1}{a^b}\)
yes i understand that...i just can't seem to get the correct answer to this...
  • phi
can you simplify \[ x ^{-5}x ^{4} \]? (add the exponents)
x^-1
  • phi
yes now we have up top \[ (x^{-1})^4 \] now use the rule multiply exponents to simplify that
X^-4
  • phi
now let's do the bottom. first \[ (x ^{4}x ^{-6}) \]
x^-2
  • phi
now (x^-2)^-5
x^10
  • phi
so we have \[ \frac{x^{-4}}{x^{10} }\]
so 1/ x^14
  • phi
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)
  • phi
yes 1/x^14 this can also be written x^(-14)
ok thank you!

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