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Please help solve the third question down (6 x5=...) and show how. 

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alexb2 | eNotes Employee

Posted October 31, 2013 at 6:13 PM via web

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Please help solve the third question down (6 x5=...) and show how. 

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2 Answers | Add Yours

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valentin68 | College Teacher | (Level 3) Associate Educator

Posted October 31, 2013 at 6:33 PM (Answer #1)

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Whenever you have a to take the n-th root from a number you need to raise that number to a fractional power having as numerator 1 and as denominator `n` . Thus

`root(6)(x^5) =(x^5)^(1/6) =x^(5*1/6) =x^(5/6)`

We have to take the 6-th root from the number `x^5` . Equivalent, we raise the number `x^5` to the power `1/6` . Then we use the powers properties to transform `(x^5)^(1/6)` into the number `x^(5/6)` .

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michuraisin | Student, College Junior | Salutatorian

Posted November 1, 2013 at 4:36 AM (Answer #2)

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Recall that:

`root(n)(x)` =`x^(1/n)`

Therefore:

`root(6)(x^5)` , where n=6 and x=`x^5`

Substitute the variables and you get

`(x^5)^(1/6)` , which can be simplified to

`x^(5/6)`

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