why does -8 squared = - 64?

think about this question

$$25-4^2$$         it is  25-16 = 9     see the minus was not squared only the 4 was squared.

 

$$-8^2$$   really means    $$-1*8^2$$     and powers are done before multiply so it is  $$-1*64 = -64$$

 

I hope that helps  :)

$$\\\textcolor[rgb]{150,0,0}{-(8^2) }= (-1)\cdot (8^2) = (-1)\cdot (8\cdot 8)= (-1)\cdot (64) \textcolor[rgb]{150,0,0}{=- 64}\\\\
\textcolor[rgb]{0,0,150}{(-8)^2 }=[(-1)\cdot(-8)]^2 = [(-1)^2 \cdot (8)^2] = ( 1\cdot 64) \textcolor[rgb]{0,0,150}{=64}$$

.

8x8=64

-8x-8=-64