jsl,

You're certainly not alone if you find multiplying or dividing decimals confusing. Writing numbers as decimals is great if you have a calculator, but decimals are often very awkward if you just have pen and paper- as you do on the GMAT. Fractions, on the other hand, are easy to deal with, if you know the basic rules for multiplying and dividing fractions. For example:

1.125/0.625 = ?

That's a bit time consuming if you work with decimals. But:

(9/8)/(5/8) = 9/5 = 1.8

is very fast. For the question you've posted, I'd certainly use kishore's approach. I'd convert the decimal to the fraction 2^6/10^6. Then, to cube root, we divide the exponents by 3. To take the positive square root, we divide again by 2. We're left with 2/10 = 0.2.

As for your question about cube rooting, note that taking the cube root of a number is the same as raising the number to the exponent (1/3). So, if we have, for example, the cube root of x^6, that's equal to:

(x^6)^(1/3)

and because of the 'tower of powers' rule, one of the basic (and most important!) powers rules, we multiply the powers here. So this is just equal to x^2. That's why the cube root of (2/10)^6 is just (2/10)^2.