anonymous
  • anonymous
Simplify the expression: \[\left( \frac{ x ^{4}y ^{8} }{ x ^{6}y ^{6}} \right)^{1/2}\] Write your answer without negative exponents.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
I'm just gonna be honest here... I look at this expression and cringe in fear. So I'm gonna need help from the ground up.
anonymous
  • anonymous
you can start by dividing each exponent by 2, since everything is being raised to the power of one half
anonymous
  • anonymous
i.e start with \[\frac{x^2y^4}{x^3y^3}\]

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anonymous
  • anonymous
then subtract the exponents of the like terms
anonymous
  • anonymous
Okay, then we add the exponents with the same bases?
anonymous
  • anonymous
no, you subtract because it is a fraction (division) if it was multiplication you would add them
anonymous
  • anonymous
Okay, so we get \[x ^{-1}y\]
anonymous
  • anonymous
since you have to write with positive exponents, subtract the smaller ones from the bigger ones
anonymous
  • anonymous
yeah that is right, what you wrote
anonymous
  • anonymous
but as i said, you want positive exponents, so i would think like this \[\large \frac{x^2y^4}{x^3y^3}=\frac{y^{4-3}}{x^{3-2}}=\frac{y}{x}\]
anonymous
  • anonymous
you got the same answer
anonymous
  • anonymous
so its just xy?
anonymous
  • anonymous
no it is what i wrote
anonymous
  • anonymous
Okay.
anonymous
  • anonymous
writing with positive exponents does not mean change the minus signs to plus signs it means use the fact that \(x^{-1}y=\frac{y}{x}\)
anonymous
  • anonymous
notice you could have done the subtractions first, like this \[\left( \frac{ x ^{4}y ^{8} }{ x ^{6}y ^{6}} \right)^{1/2}=\left( \frac{ y ^{2} }{ x ^{2}} \right)^{1/2}\] then divided the exponents by 2 either way works,whatever you think is easiest

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