anonymous
  • anonymous
Simplify the given expression to rational exponent form, justify each step by identifying the properties of rational exponents used. All work must be shown.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
@amistre64
anonymous
  • anonymous
@zkrup please helpp

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anonymous
  • anonymous
@phi
phi
  • phi
replace the cube root with an exponent 1/3 \[\sqrt[3]{a}= a^\frac{1}{3}\]
phi
  • phi
in your case, a is \( x^{-6} \)
anonymous
  • anonymous
thank youu @phi
phi
  • phi
you are not done yet.
anonymous
  • anonymous
i know im trying to figure it out ,
anonymous
  • anonymous
could you show me the steps?
anonymous
  • anonymous
@koribaby :If a number was in the radical with 2 we have : Power / 2 For example : \[\sqrt{4}= \sqrt{2^2} = 2^2/2 = 2\]
anonymous
  • anonymous
@koribaby:Got it ?
anonymous
  • anonymous
okayy alittle
anonymous
  • anonymous
One another example : \[\sqrt{8^4}\]=8^4/2=8^2 Now it s your turn : \[\sqrt{7^2}\]=?
goformit100
  • goformit100
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phi
  • phi
\[\frac{ 1 }{ \sqrt[3]{x^{-6}} }= \frac{ 1 }{(x^{-6})^\frac{1}{3}}\] now use this rule: \[ \left(a^b\right)^c = a^{bc}\] in other words, you can change the exponent to -6*1/3 = -2 \[ \frac{ 1 }{x^{-2}} \] now use one last rule \[ \frac{1}{a^{-b}} = a^b\] this rule means \[ \frac{ 1 }{x^{-2}} = x^2 \]
anonymous
  • anonymous
THX @phi

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