anonymous
  • anonymous
Rewrite in simplest radical form 1 x −3 6 . Show each step of your process.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1437531698638:dw|
anonymous
  • anonymous
@ospreytriple
anonymous
  • anonymous
First, I would reduce the exponent of x. What do you get?

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anonymous
  • anonymous
-1/2
anonymous
  • anonymous
Right on. So now you have\[\frac{ 1 }{ x ^{-\frac{ 1 }{ 2 }} }\]Is that right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
OK, I hope you will agree that\[\frac{ 1 }{ x ^{-\frac{ 1 }{ 2 }} } = \left( \frac{ 1 }{ x } \right)^{-\frac{ 1 }{ 2 }}\]You OK with that?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Perfect. Now, to invert the base, you must change the sign of the exponent. For example,\[3^{-2} = \left( \frac{ 1 }{ 3 } \right)^{2}\] or\[\left( \frac{ 1 }{ 4 } \right)^{5} = 4^{-5}\]Gwt the idea? You need to do the same thing with\[\left( \frac{ 1 }{ x } \right)^{-\frac{ 1 }{ 2 }}\]What do you get?
anonymous
  • anonymous
x to the pwer of 2?
anonymous
  • anonymous
Don't invert the exponent, just change its sign. Invert the BASE, and change the sign on the EXPONENT. Try again?
anonymous
  • anonymous
x to the power of 1/2?
anonymous
  • anonymous
Perfect. Now write it in radical form.
anonymous
  • anonymous
In general, fractional exponents are written in radical form like this:\[x ^{\frac{ a }{ b }} = \sqrt[b]{x ^{a}}\]
anonymous
  • anonymous
\[\sqrt{x}\]
anonymous
  • anonymous
Well done!
anonymous
  • anonymous
thank you again!

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