If you have $$x^3(x^2 + 1)^{-\frac{1}{2}},$$ os the power or the product calculated first? I'm assuming the power comes first but I don't like to just assume.
3 Answers
Powers have precedence over multiplication. (Powers are applied first.)
It's just like how the only thing squared in $x y^2$ is the $y$.
Exponentiation is done before multiplication, so it should not be "an assumption". Of course, the + is done before the exponentiation, unless you are planning to turn it into a series or something.
Indices before multiplication.
$$x^3(x^2 + 1)^{-\frac{1}{2}} = x^3((x^2 + 1)^{-\frac{1}{2}})$$
You can remember the order of precedence by the acronym 'BIDMAS': Brackets, Indices, Division, Multiplication, Addition, Subtraction.