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anonymous
 one year ago
Rewrite in simplest radical form
1/x^3/6. Please show each step of your process.Thank you so much
anonymous
 one year ago
Rewrite in simplest radical form 1/x^3/6. Please show each step of your process.Thank you so much

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Is this the problem? dw:1434407986067:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2First, you can reduce 3/6

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2What is the fraction  3/6 in simplest terms?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Correct. dw:1434408138951:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Do you know how to deal with a negative exponent?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Here is the rule for negative exponents: \(\Large a^{n} = \dfrac{1}{a^n} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2No. 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.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Just 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
 one year ago
Best ResponseYou've already chosen the best response.2Notice 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
 one year ago
Best ResponseYou've already chosen the best response.2dw:1434408609017:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2You see how the rule and what we have are similar?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But that wouldn't be our final answer, right?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Correct. We have one more step. We still need to deal with the fractional exponent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Here is the rule for a fractional exponent with numerator 1: \(\Large a^{\frac{1}{n}} = \sqrt[n]{a} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2A fractional exponent is a root. The denominator tells you which root it is.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2dw:1434408876045:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2That is the final answer. Here are all the steps in one single drawing: dw:1434408951600:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what happened to the 1/2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathstudent55 sorry :) I'm just curious!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathstudent55 Is there a certain rule for this up above?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathstudent55 please helppp

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2@JasperRayWolfAlysa88 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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