Solving for Equality with Positive a and b

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hello everyone,

I have a problem, if anyone can get me started. Thanks

I have to show this equality knowing that a and b are positive and they do not euqal 0:

(a^{2}+a^{\frac{4}{3}}b^{\frac{2}{3}})^{\frac{1}{2}} + (b^{2}+a^{\frac{2}{3}}b^{\frac{4}{3}})^{\frac{1}{2}} =(a^{\frac{2}{3}}+b^{\frac{2}{3}})^{\frac{3}{2}}

now I have no idea where to start!
 
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Anyone please?
 
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Hellooo?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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