Negative Number Raised to a Power

[BlindVision]

Can someone refresh me on a rule or illustrate the logic that a negative number raised to any power still yields a negative answer?

examples:

-2^2 = -4

-2^5 = -32

-3^2 = -9

-3^3 = -27

[cramya]

(negative integer) raised to (even positive power) is positive.


(-2) ^ 2 = 4 (not -4 as stated above)

(-2) ^ 4 = 16

(negative integer) raised to (odd positive power) is negative

(-2)^3 = -8
(-2)^1 = -2

Hope this helps.

[Bhattu]

(negative integer) raised to (even positive power) is positive.


-2 ^ 2 = 4 (not -4 as stated above)

-2 ^ 4 = 16

(negative integer) raised to (odd positive power) is positive.

-2^3 = -8
-2^1 = -2

Hope this helps.

I think there was a typo, shouldn't it be = (negative integer) raised to (odd positive power) is negative?

[Ian Stewart]

(negative integer) raised to (even positive power) is positive.

-2 ^ 2 = 4 (not -4 as stated above)

Here, it really depends on how the expression is written. If you raise -2 to the power of 2, the answer is certainly positive 4. That is, if you have:

(-2)^2

that is equal to 4, because this is equal to (-2)*(-2). However, if the negative is not enclosed in brackets, as was written in the original post:

-2^2

then by order of operations (BEDMAS), we must raise 2 to the power 2 first, then take the negative of that. So, if there are no brackets,

-2^2 = -4

because this is equal to -(2)*(2).

[Bhattu]

Thanks for that - helps clarify that for me and also probably a careless error I should be aware of

[BlindVision]

then by order of operations (BEDMAS), we must raise 2 to the power 2 first, then take the negative of that. So, if there are no brackets,

-2^2 = -4

because this is equal to -(2)*(2).

What does the "B" in "BEDMAS" stand for? "Brackets"? Thank you!

[Ian Stewart]

then by order of operations (BEDMAS), we must raise 2 to the power 2 first, then take the negative of that. So, if there are no brackets,

-2^2 = -4

because this is equal to -(2)*(2).

What does the "B" in "BEDMAS" stand for? "Brackets"? Thank you!

Yes, 'brackets'. The mnemonic is sometimes presented as 'PEDMAS', where the P stands for 'parentheses'.

[cramya]

Thanks Ian.


Bhattu, I have corrected the typo.

Regards,
CR