How would you simplify this? $\left(a^{0.5} + b^{0.2}\right)^{-0.4}$ 
How would you simplify this?
$$\left(a^{0.5} + b^{0.2}\right)^{-0.4}$$

This isn't the normal $(a + b)^2$ or $(a+b)^3$.
So, I'm a little confused.
 A: I personally would not simplify this. 
Often it is not really clear what you consider a 'simplification' of a certain term. 
It depends on what you are trying to do.
Take for example a polynomial function:
$f(x)=x^4+3x^3+3x^2+x$
this can be simplified to $f(x)=x(x+1)^3$ which is a nice and compact form. But if you want to find the derivative it is simpler to use the first variante, because taking that derivative is trivial compared to the use of the product rule of the second form.
But when you want to find the roots, you would prefere the second form over the first.
The art is to manipulate the term in specific ways to make your life easy.
I personally do not like negative exponents. Also I prefer fractions over decimals (most of the time), but I would not touch your term in any way. Would only make it worse.
A: What you could do at most is -
$\displaystyle (a^{\frac{1}{2}}+b^{\frac{1}{5}})^{- \frac{2}{5}}= \frac{1}{(a^{\frac{1}{2}}+b^{\frac{1}{5}})^{\frac{2}{5}}}=\frac{1}{\sqrt[5]{(a+b^{\frac{2}{5}}+2a^{\frac{1}{2}} b^{\frac {1}{5}})}}$
A: Just like Cornman had said, it is unwise to "simplify" the said expression $(a^(0.5)+b^(0.2))^(-0.4)$. In fact, if you define "simplify" as to condense the expression as much as possible, then it is already simplified.
Using Wolfram Alpha to test it out, this is the result. As you can see, "simplifying" (ie breaking the bracket and the exponent) is very annoying and counterproductive. Therefore, just leaving it as what it is now. The only "simplifying" I recommend is to re-arrange the term
$\large\frac{1}{\left(a^{\frac{1}{2}}+b^{\frac{1}{5}}\right)^{\frac{2}{5}}}$
question: does anyone knows how to type fractions here? Thanks [ANSWERED - Thanks for your help]
A: The exponents in this case are rational, instead of integral. By your references to integral powers of binomials, it seems by simplify you mean expand. If you do that in this case, the expansion would not be valid for all values of $a$ and $b,$ since it would develop into an infinite series. If you still consider that a simplification (depending on what you want to do with the expression) then go ahead to expand it by using the binomial theorem.
