Final answer:
The provided question seems to contain a typo or missing information, making it impossible to determine the exact product. The principles of adding exponents and understanding square roots as fractional powers can be applied if the full expression is known. The question also references trigonometry identities and the quadratic equation, but these do not seem directly relevant to the calculation of the product.
Step-by-step explanation:
The question asks for the product of a complex expression involving variables x and y with given powers. From the details provided, it seems there is a typo or a part of the question is missing which makes it challenging to accurately determine the required product. However, if we use the information provided, we can discuss the general method of multiplying terms with exponents.
When multiplying terms with the same base, we add the exponents. For example, xa * xb = xa+b. When dealing with square roots, we can treat them as fractional exponents, so sqrt(x) = x1/2 and x2 = sqrt(x). Unfortunately, with incomplete product information, we cannot provide a definitive answer.
Additionally, the question seems to reference trigonometric identities and laws of sines and cosines when listing sin 20, cos 20, and other trigonometric functions. These are important formulas used to solve various trigonometry problems in triangles. It is also worth mentioning the quadratic equation and its standard form at2 + bt + c = 0, as well as using the quadratic formula to find its solutions.