How do I simplify (v/pi)(2pi/v)2/3 to 2(v/2pi)1/3?

[JOhnJDC]

Homework Statement

Please help me understand how (v/pi)(2pi/v)^2/3 equals 2(v/2pi)^1/3

This is from my book.

The Attempt at a Solution

[(v)(2^2/3)(pi^2/3)]/v^2/3pi = 2^2/3(v/pi)^1/3

What am I doing wrong? Thanks.

EDIT: I made a mistake in copying over my attempt; fixed now.

 

[JOhnJDC]

I'm beginning to think that my book is wrong and that my attempt is correct. Can anyone confirm?

 

[Mentallic]

You are both correct

 

[JOhnJDC]

You are both correct

I don't see how 2^2/3(v/pi)^1/3 = 2(v/2pi)^1/3 Can you explain?

 

[Mentallic]

$$2^{2/3}=2^{1-1/3}$$

does it seem obvious now?

 

[JOhnJDC]

$$2^{2/3}=2^{1-1/3}$$

does it seem obvious now?

Yes--I see it now. Thanks, Mentallic.