Order of precedence: in $ab^{c}$, which operation goes first?

Question

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.

Answer 1

Powers have precedence over multiplication. (Powers are applied first.)

It's just like how the only thing squared in $x y^2$ is the $y$.

Answer 2

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.

Answer 3

Indices before multiplication.

$$x^3(x^2 + 1)^{-\frac{1}{2}} \Longleftrightarrow x^3((x^2 + 1)^{-\frac{1}{2}})$$

You can remember the order of precedence by the acronym 'BIDMAS': Brackets, Indices, Division, Multiplication, Addition, Subtraction.