Question

Why does -2 to the power of 3 produce the same answer as (-2) to the power of 3

Answer 1

The way to put this is that any negative base raised to an odd-numbered power, will result in a negative result, whereas any negative base raised to an even-numbered power, will result in a positive result, with the EXCEPTION of a negative base written WITHOUT grouping symbols. For instanse:

`\displaystyle -1000 = -10^3 \\ -1000 = [-10]^3 \\ \\ BUT \\ \\ 10000 ≠ -10^4\:[-10000 = -10^4] \\ 10000 = [-10]^4`

I hope you know the differense now, and as always, I am joyous to assist anyone at any time.

Answer 2

because it's an odd exponent

Explanation:

-2^3 = -(2*2*2)

(-2)^3 = (-2)*(-2)*(-2)

if it was ^4 the sign would be flipped:

-2^4 = -(2*2*2*2) = -16

(-2)^4 = (-2)*(-2)*(-2)*(-2) = 16