Fractional exponents problem help.

[8dltndus]

I am confused about this question.:
the formula for the surface area of a sphere S in theres of its volume V is
S=(4*pi)squared to the 1/3(3V)squared to the 2/3.what is the surface area of the sphere that has a volume of 36*pi cm{to the third}
Leave the symbol pi in your answer. What do you notice?

I've been trying to solve this problem for hours now, and 'i just can't get it because I cannot find the third root of a decimal..
and i need a hint..
please help. i have no problem with the normal questions but this problem was a "challenge and extend" question.

 

[Deleted member 4993]

I am confused about this question.:
the formula for the surface area of a sphere S in theres of its volume V is
S=(4*pi)squared to the 1/3(3V)squared to the 2/3.what is the surface area of the sphere that has a volume of 36*pi cm{to the third}
Leave the symbol pi in your answer. What do you notice?

I've been trying to solve this problem for hours now, and 'i just can't get it because I cannot find the third root of a decimal..
and i need a hint..
please help. i have no problem with the normal questions but this problem was a "challenge and extend" question.

\(\displaystyle S \ = \ (4\pi)^{\frac{1}{3}}(3V)^{\frac{2}{3}}\)

\(\displaystyle S \ = \ (4\pi)^{\frac{1}{3}}(3*36\pi)^{\frac{2}{3}}\)

\(\displaystyle S \ = \ (4\pi)^{\frac{1}{3}}(3*9*4\pi)^{\frac{2}{3}}\)

\(\displaystyle S \ = \ (4\pi)^{\frac{1}{3}}* (4\pi)^{\frac{2}{3}}(27)^{\frac{2}{3}}\)

\(\displaystyle S \ = \ (4\pi)^{\frac{1}{3}}* (4\pi)^{\frac{2}{3}}(3^3)^{\frac{2}{3}}\)

There is "really" no third root of a decimal. So finish it.....