Does an exponent apply to an entire term or is BIDMAS applied in the term? Me and a mate of mine are having a small debate, because I don't know if I'm being incredibly stupid or not.
If you take a term, $ax^b$, does the exponent '$b$' apply to the entirety of $ax$, making it $(ax)^b$, or just $x$, making it $a(x^b)$?
It's silly to debate over something that is probably basic mathematical law, but I don't know if I'm wrong or not.
My argument is that because an exponent/indice will always precede multiplication, and that $ax$ isn't just a constant number, it's the product of a and $x$, that the exponent '$b$' will only apply to $x$, and not $ax$ - or at least that the exponent '$b$' will apply to '$x$' BEFORE the multiplication of '$a$' and '$x$' can take place.
Am I wrong?
 A: Do the product after the exponent, unless brackets tell you otherwise
A: You are correct.  If you and your friend have studied polynomials, this will be familiar in an example like $5x^2$ which means $5\cdot(x^2)$.  And $(5x)^2=25x^2$ is different.
A: You're right - (I)ndices come before (M)ultiplication, so you raise $x$ to the power $b$, then multiply by $a$.
A: You are right, for the reasons you explained. 
But perhaps the more important take-away is that "BIDMAS" is not a 'law', it's just something we decided among one another to make communication easier. If your friend and you reach a misunderstanding about what the math you write means, maybe you should agree together what you mean, or use more parentheses to be clear.
Mathematicians among one another noticed that they wanted to write $a \times (x^b)$ much more often than $(ax)^b$, so they reserved the shorter notation for the former, and this gets taught to high school students as BIDMAS (or similar).
A: Generally:
$$ax^b\equiv a\cdot x^b$$
while:
$$(ax)^b\equiv a^b\cdot x^b$$
