Is there a difference between (x)^3 vs x^3?
For example, is (-2)^3 the same as -2^3?
And I think it is different if it is -(2)^3, is that correct?
(x)^3 is exactly the same as x^3
(-2)^3 = (-2)(-2)(-2) = -8
-2^3 = -(2)^3 = -(2*2*2) = -8
works ok for odd powers, but not for even ones.
Steve,
Just to make sure I understand, could you check if this is correct..
(-2)^4 = 16
-(2)^4 = -16
correct. As is -2^4 = -16
Yes, there is a difference between (x)^3 and x^3.
In mathematics, a positive exponent indicates that the base (x) is multiplied by itself the number of times specified by the exponent. So, x^3 means "x multiplied by itself three times."
To answer your specific examples:
1. (-2)^3 is different from -2^3. When you put parentheses around a negative number before raising it to a power, the negative sign is also cubed. In this case, (-2)^3 means "(-2) multiplied by itself three times." This results in -8 as (-2) * (-2) * (-2) = -8.
2. On the other hand, -2^3 is computed differently. Without parentheses around -2, you first calculate the exponent and then apply the negative sign. So, -2^3 means "-(2 cubed)." This results in -8 as 2 * 2 * 2 = 8, and then the negative sign is applied.
Therefore, (-2)^3 is -8, -2^3 is -8 as well, and -(2)^3 is -8.