SOLUTION: How would you put this into radical form: (8x)2/3.

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Question 487734: How would you put this into radical form: (8x)2/3.

Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
(8x)^(2/3) is equal to ((8x)^(1/3))^2
you get the cube root of (8x) and then you square it.
in radical form, this would be shown as:

(8x)^(2/3) is also equal to ((8x)^2)^(1/3)
you square (8x) and then you take the cube root of it.
in radical form, this would be shown as:

you'll get the same answer either way.
assume x = 27
the first form gets the cube root of 27 which is equal to 3 and then squares that to get 9.
the second form squares 27 to get 729 and then takes the cube root of that to get 9.

Answer by ikleyn(52867)   (Show Source):
You can put this solution on YOUR website!
.
How would you put this into radical form: (8x)2/3.
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The solution and the answer in the post by @Theo both are incorrect.

The correct answer is   .

Indeed, you can consider (8x)^(2/3) as the square of the cube root of (8x)^(1/3).

Doing this way, you will get    = = .

Alternatively, you can consider (8x)^(2/3) as the cube root of (8x)^2 = 64x^2.

Doing this way, you will get    = .

Thus, either way leads to the same answer   .

Solved correctly.

Answer by MathTherapy(10556)   (Show Source):
You can put this solution on YOUR website!

How would you put this into radical form: (8x)2/3. = = = =