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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.

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the only thing raised to the $-1/2$ is the $x^2+1$ – yoyo Apr 17 '11 at 18:19
up vote 3 down vote accepted

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

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

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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.

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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.

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