Which of the following is equal to the square root of the cube root of 5? 5 to the power of 1 over 3 5 to the power of 1 over 6 5 to the power of 2 over 3 5 to the power of 3 over 2

5 to the power of 1 over 6

or as an expression:  

First we are going to express our statement as an algebraic expression:

square root of the cube root of 5 =

Next, we are using laws of radicals to simplify our expression:

Law of radicals:

We can infer from our expression that n=2, m=3, and a=5, so lets replace the values:

Now, to express the radical as exponent, we are going to use another law of radicals:

Law of radicals:

Just like before, we can infer for our expression that n=6 and a=5, so let's replace the values:

And in words:

square root of the cube root of 5 is equal to 5 to the power of 1 over 6

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x