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

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SUMMARY

The expression (v/pi)(2pi/v)^(2/3) simplifies to 2(v/2pi)^(1/3) through the application of exponent rules and algebraic manipulation. The key steps involve recognizing that 2^(2/3) can be rewritten as 2^(1 - 1/3), which clarifies the relationship between the two expressions. The discussion confirms that both the original expression and the simplified form are indeed correct, resolving the initial confusion regarding the simplification process.

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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)(22/3)(pi2/3)]/v2/3pi = 22/3(v/pi)1/3

What am I doing wrong? Thanks.

EDIT: I made a mistake in copying over my attempt; fixed now.
 
Last edited:
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I'm beginning to think that my book is wrong and that my attempt is correct. Can anyone confirm?
 
You are both correct :wink:
 
Mentallic said:
You are both correct :wink:

I don't see how 22/3(v/pi)1/3 = 2(v/2pi)1/3 Can you explain?
 
Last edited:
2^{2/3}=2^{1-1/3}

does it seem obvious now?
 
Mentallic said:
2^{2/3}=2^{1-1/3}

does it seem obvious now?

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

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