Say you have a POSITIVE number, for example, ‘2’. When you add an exponent onto this positive number, the answer will ALWAYS be a postive number:

2² = 2 x 2 = 4

2³ = 2 x 2 x 2 = 4 x 2 = 8

When you have a NEGATIVE number with an exponent, the outcome may be positive or negative, depending on the value of the exponent.

When multiplying an EVEN number of ‘negatives’, the answer will ALWAYS come out POSITIVE:

-2² = -2 x -2 = 4

When multiplying an ODD number of ‘negatives’, the answer will ALWAYS come out NEGATIVE:

(I’ll do this one in steps):

-2³ = -2 x -2 x -2 = multiply -2 x -2. You get ‘4’. SO…

4 x -2 = -8

I can’t help you with the other question because I don’t understand the equation…. If it’s 2(-9), then you multiply ‘-9’ by 2 …..(-9 x 2 = -18) – – – Remember, there’s an odd number of negatives (only one negative: -9 ), so the answer has to be negative.

An exponent multiplies a number by itself. A negative times a negative is always a positive. So a negative number raised to the second power equals a positive number.

-2^2=4

Now assuming that the second question is -9², then it’s the same type of thing….-9*-9=81

If it’s 2^-9 then it’s more complicated. Raising to a negative power means you have to change it to 1/the number^positive exponent.

Here it would be 1/(2^9). Or 1/(2*2*2*2*2*2*2*2*2)

1/512

Does that help you out?