I am trying to help my sibling with math but their teacher seems to want an absolute value inside the radical when simplifying the radical's power, not just outside, which some teachers care and some don't. I am not sure how to do it.
One example problem here:
I got $ \ x · \sqrt{5xy} \ $ but the teacher said absolute values should be in some answers. I assume the answer was $ \ x · \sqrt{5|x||y|} \ . \ $ I first simplified the $ \ x^{12} \ $ and then converted the radicals to fractional exponents, which were both 4/8 and then simplified them to 1/2.
Another problem:
I obtained $ \ 2 · x^4 · y^9 · \sqrt[4]{2^2} · \sqrt[4]{x^2} \ \ . \ $ I assume this answer would be $ \ 2 · x^4 · y^9 · \sqrt{2|x|} \ \ . $
Do you add an absolute value after simplifying a fractional exponent if the base is a variable? I cannot find any examples of this anywhere online. Does anyone have an example of a problem where there are absolute values inside the radical?