Hello forum, Vaironxxrd here.

I have a question about exponents. If I have,

$\displaystyle (-9)(-9)^3$ Would that be $\displaystyle (-9)^4$ or $\displaystyle (-9^4)$.

If possible can you guys provide other examples?

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- Oct 8th 2011, 07:47 AMvaironxxrdevaluating numerical expression
Hello forum, Vaironxxrd here.

I have a question about exponents. If I have,

$\displaystyle (-9)(-9)^3$ Would that be $\displaystyle (-9)^4$ or $\displaystyle (-9^4)$.

If possible can you guys provide other examples? - Oct 8th 2011, 07:57 AMSironRe: evaluating numerical expression
It's indeed $\displaystyle (-9)^4$. For example, consider $\displaystyle (-2)^4\cdot (-2)^2$ which is offcourse $\displaystyle (-2)^6=64$ and $\displaystyle -2^6=-(2^6)=-64$ therefore there're not equal.

So it's important to use brackets! - Oct 8th 2011, 09:54 AMvaironxxrdRe: evaluating numerical expression
- Oct 8th 2011, 09:58 AMe^(i*pi)Re: evaluating numerical expression
Exponents come before multiplication in the order of operations and a minus sign in front is multiplying by -1.

However, brackets come before exponents so if the multiplication is done*inside*the bracket it too is affected by the exponents.

$\displaystyle (-9)^2 = -9 \times -9 = 81 \text{ OR } (-9)^2 = (-1 \times 9)^2 = (-1)^2 \times 9^2 = 81$

$\displaystyle -9^2 = -1 \times 9^2 = -81$ - the brackets here are unnecessary and only serve to complicate matters IMO. - Oct 8th 2011, 10:02 AMvaironxxrdRe: evaluating numerical expression
- Oct 8th 2011, 10:06 AMFrameOfMindRe: evaluating numerical expression
Remember BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction).

The order of operands is very important, and this is where you're having trouble.

-9 is essentially like saying 0 - 9, you just omit the 0.

Now, from BIDMAS, we know that everything in brackets is evaluated first, and that indices/multiplication is evaluated before subtraction.

So (-9^2) is like saying (0 - 9^2). You evaluate the index first, then you subtract the result from 0.

0 - (9)(9) = 0 - 81 = -81

Whereas, in (-9)^2 you evaluate everything in brackets first, so (0 - 9)^2 = (-9)(-9) = 81, because multiplying an even number of negatives together results in a positive.

I hope that was clear enough. - Oct 9th 2011, 07:34 AMvaironxxrdRe: evaluating numerical expression
- Oct 9th 2011, 07:41 AMskeeterRe: evaluating numerical expression
- Oct 9th 2011, 07:43 AMvaironxxrdRe: evaluating numerical expression
Yeah sorry for that. Does it matter how many threads I start? I feel like it might be annoying.

- Oct 9th 2011, 07:55 AMskeeterRe: evaluating numerical expression