How do you solve 32^-1/5 ?? In case thats confusing how do you solve 32 to the negative one fifth power. Please please explain and show work. Thank you!

Sorry...misread the question originally:

   32(-1/5) =  sqrt5(1/32) = sqrt5( 1/2 x 1/2 x 1/2 x 1/2 x 1/2)  = 1/2

 #1 ElectricPavlov:

You got the right answer, but how did you get 1/2 out of:sqrt(5){1/2^5}??!!.

32^(-1/5)=1/[32^(1/5)]=1/2.

Sorry for the unclarity:    sqrt5 means '5th root'   

so sqrt5 (x^5)  = x   right?

Then sqrt5(1/2 x  1/2 x 1/2 x 1/2 x 1/2)  =  sqrt5( ( 1/2)^5 )  = 1/2  

ElectricPavlov:

Sorry young man!!. But, you still didn't get it right!. This expression: 32^(-1/5) means: the 5th root of 32, which is =2. But because 5th root is negative, that means you take the RECIPROCAL of 5th root of 32, which is: 1/2.

ElectricPavlov:

This is your final answer in # 3 above:=  sqrt5( ( 1/2)^5 )  = 1/2. Now, let us evaluate it step by step:

Get rid of the inner brackets: ( 1/2)^5=0.03125. Now, you have this:sqrt(5) x 0.03125. Next, take the square root of 5=2.23606......... x 0.03125=0.069877.....etc. Does this last answer =1/2???. Do you see it?.

Answer #3 above was a continuation of answer #1 after the questioner asked how I got my answer...Read that one too....

sqrt5(1/32) = sqrt5((1/2)^5)) = 1/2 !!!!

( 1/2)^5 = .03125        AND  sqrt5(.03125) = 1/2   !!!!

What is the problem YOU are having?????

ElectricPavlov:

I see where the confusion is!. When you write this: sqrt5(.03125) = 1/2. It means you take the square root of 5 X .03125. What you want to write is this: The 5th root of .03125, which you can write as:(.03125)^(1/5), which will give you 1/2. Write 1/5 as 0.2, or: (.03125)^0.2=1/2. Try it on the calculator.

Sorry for your confusion.....people often ask questions on this forum   like the cube root of 27 and ask it like:

sqrt3 (27)       I was doing the same thing   sqrt5 (32)  MEANS the 5th root of 32.      Thought that was clear to everyone....guess not.....