Exponential doubt

(-2) ^ 4 = +16

- (2)^4 = -16.

The difference between the above two expressions is that the negative sign is inside the parenthesis in the first expression and outside the parenthesis in the second expression.

1st expression can also be written as (-1)^4 * (2)^4 = 1 * 16 = +16
2nd expression can be written as: (-1)^1 * (2)^4 = (-1) * (16) = -16

In the second expression, the exponent 4 ONLY APPLIES TO '2' not '-2' since there aren't any parenthesis around the whole expression. You have to assume the exponent only applies to the number '2' and not '-2'.

Notice that the second expression is negative because the negative sign is outside of the parenthesis and the positive exponent (in this case, 4) doesn't affect it whereas in the first expression the positive exponent 4 DOES affect it.

However, if you have an ODD EXPONENT, then it does not matter, the final answer will always be negative. For example:

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

But it is still recommended that you USE PARENTHESIS just to make life easier and questions less complicated for you.