calculusxy
  • calculusxy
Question with exponents! Question attached below...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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calculusxy
  • calculusxy
\[\huge \frac{ (-xy^4)^{-4} }{ -2x^3 \times x^2y^3 }\]
Jhannybean
  • Jhannybean
\[(-2x^3)(x^2y^2) \implies -2 \cdot x^{3+2} \cdot y^2 =~?\]
calculusxy
  • calculusxy
i got the answer of \[\frac{ 1 }{ 2x^9y^19 }\] but the answer key says that it's negative.. i don't know why

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Jhannybean
  • Jhannybean
Alright let's check each step.
Jhannybean
  • Jhannybean
what would you get for : \(\color{#0cbb34}{\text{Originally Posted by}}\) @Jhannybean \[\large (-2x^3)(x^2y^2) \implies -2 \cdot x^{3+2} \cdot y^2 =~?\] \(\color{#0cbb34}{\text{End of Quote}}\)
calculusxy
  • calculusxy
\[\large -2x^5y^2\]
Jhannybean
  • Jhannybean
Alright, and when you distribute the \(-4\) power into every term in the ( ), you expand it like so: \[\large (-xy^4)^{-4} \implies (-x)^{-4} \cdot (y^4)^{-4} = ~?\]
calculusxy
  • calculusxy
\[\large -x^{-4} \times y^0\]
calculusxy
  • calculusxy
which is basically like \[\large -x^{-4}\]
calculusxy
  • calculusxy
\[\large \times \] do you mean this symbol? if so, it's multiplication.
Jhannybean
  • Jhannybean
be careful, you wouldnt be adding the exponents here, you'd be multiplying them. \[\large (y^4)^{-4} = y^{4( -4)}\qquad (y^4)^{-4} \ne y^{4-4}\]
calculusxy
  • calculusxy
oh yes
calculusxy
  • calculusxy
i still don't understand how you got the negative...
calculusxy
  • calculusxy
yeah or whose ever work that was posted in the 3 parts
just_one_last_goodbye
  • just_one_last_goodbye
pretty fast eh? ^_^ thinking about making it a tool on OS as an extention
Jhannybean
  • Jhannybean
defeats the purpose of Openstudy then.
calculusxy
  • calculusxy
can you please help me understand why it is a negative?
Jhannybean
  • Jhannybean
Ok cotinuing from where we left off.
Jhannybean
  • Jhannybean
I just realized theres an easier way to simplify the numerator, check this out
Jhannybean
  • Jhannybean
Instead of expanding our numerator first, we can basically turn our entire term WITH the negative exponent into a positive one. \[\large (-xy^4)^{-4} \implies \dfrac{1}{(-xy^4)^4}\] you see how the negatives in the numerator would go away?
Jhannybean
  • Jhannybean
So now we expand our numerator, and we get: \[\large \frac{1}{x^4y^{16}}\]
Jhannybean
  • Jhannybean
Now we put it over our denominator: \[\large \dfrac{\dfrac{1}{x^4y^{16}}}{-2x^5y^3}\qquad \implies \qquad \dfrac{1}{-2x^{4+5}y^{16+3} } \]
Jhannybean
  • Jhannybean
Now whether we have the negative in the numerator OR denominator, it doesnt matter, the fraction altogether is STILL negative.
Jhannybean
  • Jhannybean
Do you follow, @calculusxy ?
calculusxy
  • calculusxy
i am still trying to grasp this.
calculusxy
  • calculusxy
if we have like complex fractions, then we would have to add the exponents n put it over one?
Jhannybean
  • Jhannybean
The only reason we did that, was because we treated \((-xy^4)\) as like a variable... let' say all that junk \(=a\). And then... a is raised to a negative power, and how would we turn that power positive? by putting it over 1. \(a^{-1} \iff \dfrac{1}{a}\)
Jhannybean
  • Jhannybean
So if we have a FRACTION in the numerator, and we're DIVIDING it by a term or terms in the denominator, we follow this rule: \[\dfrac{\dfrac{a}{b}}{c} \implies \frac{a}{bc}\]
calculusxy
  • calculusxy
okay...
calculusxy
  • calculusxy
i have one other question..
calculusxy
  • calculusxy
thanks for helping me understand that
Jhannybean
  • Jhannybean
Which art are you stuck on? WE'll go from there.
Jhannybean
  • Jhannybean
part*
calculusxy
  • calculusxy
so this time i am getting a negative, but it says that it's a positive. \[\large -\frac{ ba^0 \times -a^3b^3 }{ (ab^0)^{-4} }\]
calculusxy
  • calculusxy
so i got \[\large -a^7b^4\] but the answer key simply says \[\large a^7b^4\]
calculusxy
  • calculusxy
@Jhannybean
calculusxy
  • calculusxy
@jim_thompson5910
calculusxy
  • calculusxy
@jim_thompson5910 it's the second expression w/ exponents.
jim_thompson5910
  • jim_thompson5910
calculusxy
  • calculusxy
oh okay thx !

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