How do I simplify this algebra equation?

Question

h = 16/pi(4/pi)^(2/3)

I was asked by my professor to not solve and give an approximation but to simplify for h and leave the (pi) alone

Answer 1

h = 16 / pi(4 / pi)^2/3

Apply power rule (a / b)^x = a^x / a^y

h = 16 / pi(4^2/3 / pi^2/3)

h = 16 / (pi / pi^2/3(4^2/3)

Apply power rule (a / a^2/3 = a^1-2/3

h = 16 / (pi^1-2/3)(4^2/3)

h = 16 / (pi^1/3)(16^1/3)

h = 16^1-1/3 / (pi)1/3

h = 16^2/3 / pi^1/3

h = 256^1/3 / pi^1/3

Apply power rule (a / b)^1/3 = a^1/3 / b^1/3

Therefore h = (256 / pi)^1/3.

Answer 2

h = (16/π)(4/π)^2/3

= 16* π^(-1)*4^(2/3) * π^(2/3)

= (16 * ∛4² ) π^(-1/3)

= 32 ∛2 / ∛π

that's 32 times cube root of 2 over cube root of pi.

Source: http://answers.yahoo.com/

Comments

Simplify for h, the equation h = (16/π)(4/π)^2/3

h = (32 ∛2)  (π)^(-5/3).

Answer 3

h = (16/π)(4/π)^2/3

= 16* π^(-1)*4^(2/3) * π^(-2/3)

= (16 * ∛4² ) π^(-1-2/3)

= (16 * ∛4² ) π^(-1-2/3)

= (32 ∛2)  (π)^(-5/3)