calculusxy
  • calculusxy
exponents...
Mathematics
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calculusxy
  • calculusxy
exponents...
Mathematics
schrodinger
  • schrodinger
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calculusxy
  • calculusxy
\[\huge \frac{ (x^4y^{-2})^{-3} }{ 2x^{-2}y^2x^4 }\]
calculusxy
  • calculusxy
Answer: \[\large \frac{ y^{14} }{ 2x^{14} }\]
calculusxy
  • calculusxy

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anonymous
  • anonymous
some mistake here
Jhannybean
  • Jhannybean
\[(x^4y^{-2})^{-3} \iff \frac{1}{(x^4y^{-3})^3}\]
calculusxy
  • calculusxy
sorry \y^4/2x^{14}
Jhannybean
  • Jhannybean
\[\dfrac{\dfrac{1}{(x^4y^{-3})^3}}{2x^{-2}y^2x^4}\]
calculusxy
  • calculusxy
\[\frac{ y^4 }{ 2x^{14} }\]
Jhannybean
  • Jhannybean
Did you need help solving it or just checking to see if it was correct?
calculusxy
  • calculusxy
checking
Jhannybean
  • Jhannybean
alright
Jhannybean
  • Jhannybean
\[\dfrac{\dfrac{1}{(x^4y^{-3})^3}}{2x^{-2}y^2x^4} = \dfrac{\dfrac{1}{x^{12}y^{-9}}}{2x^{-2}y^2x^4} =\frac{1}{2x^{12-2+4}y^{-9+2}}=\frac{1}{2x^{14}y^{-7}}=\frac{y^{7}}{2x^{14}} \]
Jhannybean
  • Jhannybean
Youve asked a similar question like this before. Hope this method makes sense to you.
calculusxy
  • calculusxy
here's my way: \[\frac{ (x^4y^{-2})^{-3} }{ 2x^{-2}y^2x^4 } = \frac{ x^{-12}y^6 }{ 2x^2y^2 } = \frac{ y^4 }{ 2x^{14} }\]
Jhannybean
  • Jhannybean
hmm... somehow i miscalculated the \(y\)
Jhannybean
  • Jhannybean
trial 2: \[\begin{align}\frac{ (x^4y^{-2})^{-3} }{ 2x^{-2}y^2x^4 } &= \dfrac{\dfrac{1}{\left(\dfrac{x^4}{y^2}\right)^3}}{2x^{-2}y^2x^4} \\&= \dfrac{\dfrac{1}{x^{12}y^{-6}}}{2x^{-2}y^2x^4} \\&=\dfrac{\dfrac{1}{x^{12}y^{-6}}}{2x^{2}y^2} \\ &=\dfrac{1}{(x^{12}y^{-6})(2x^2y^2)} \\&= \frac{1}{x^{12+2}y^{-6+2}} \\&= \color{red}{\frac{y^4}{x^{14}}}\end{align} \]
Jhannybean
  • Jhannybean
Sorry Im not that great at simplifying exponents :\
Jhannybean
  • Jhannybean
Typo again! I forgot the 2. \[\frac{y^4}{2x^{14}}\]

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