anonymous
  • anonymous
Rewrite in simplest radical form 1/x^-3/6. Please show each step of your process.Thank -you so much
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@peachpi
mathstudent55
  • mathstudent55
Is this the problem? |dw:1434407986067:dw|
anonymous
  • anonymous
yes:)

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More answers

mathstudent55
  • mathstudent55
First, you can reduce 3/6
mathstudent55
  • mathstudent55
What is the fraction - 3/6 in simplest terms?
anonymous
  • anonymous
-1/2
mathstudent55
  • mathstudent55
Correct. |dw:1434408138951:dw|
mathstudent55
  • mathstudent55
Do you know how to deal with a negative exponent?
mathstudent55
  • mathstudent55
Here is the rule for negative exponents: \(\Large a^{-n} = \dfrac{1}{a^n} \)
anonymous
  • anonymous
1/x^2
anonymous
  • anonymous
Right?
mathstudent55
  • mathstudent55
No. There are two things with the exponent of x we need to deal with. 1. It is a negative exponent. 2. The exponent is a fraction. Let's deal only with the negative sign on the exponent for now.
anonymous
  • anonymous
Ok:)
mathstudent55
  • mathstudent55
Just like the rule above of negative exponents works, this one also works: \(\Large \dfrac{1}{a^{-n}} = a^n \) A negative exponent in the denominator, is a positive exponent in the numerator.
mathstudent55
  • mathstudent55
Notice we have a similar thing to this last rule. We have a fraction with 1 over. Then in the denominator we have x to a negative exponent. It changes into just x to the positive exponent in the numerator, and the denominator disappears.
mathstudent55
  • mathstudent55
|dw:1434408609017:dw|
mathstudent55
  • mathstudent55
You see how the rule and what we have are similar?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
But that wouldn't be our final answer, right?
mathstudent55
  • mathstudent55
Correct. We have one more step. We still need to deal with the fractional exponent.
mathstudent55
  • mathstudent55
Here is the rule for a fractional exponent with numerator 1: \(\Large a^{\frac{1}{n}} = \sqrt[n]{a} \)
mathstudent55
  • mathstudent55
A fractional exponent is a root. The denominator tells you which root it is.
mathstudent55
  • mathstudent55
|dw:1434408876045:dw|
anonymous
  • anonymous
I see. I see
mathstudent55
  • mathstudent55
That is the final answer. Here are all the steps in one single drawing: |dw:1434408951600:dw|
anonymous
  • anonymous
what happened to the 1/2?
anonymous
  • anonymous
@mathstudent55 sorry :) I'm just curious!
anonymous
  • anonymous
@mathstudent55 Is there a certain rule for this up above?
anonymous
  • anonymous
@mathstudent55 please helppp
mathstudent55
  • mathstudent55
@JasperRayWolf-Alysa88 We used two rules that I wrote above: \(\large a^{-n} = \dfrac{1}{a^n} \) \(\large a^{\frac{1}{n}} = \sqrt[n] a\)

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