If $a^{p}\cdot b^{p}= (a\cdot b)^{p}$ then why $-1^{2}\cdot 3^{2}\neq (-1\cdot 3)^{2}$

Question

If $a^{p}\cdot b^{p}= (a\cdot b)^{p}$ then why $$-1^{2}\cdot 3^{2}\neq (-1\cdot 3)^{2}\\ -1\cdot 9\neq (-3)^{2}\\ -9\neq 9$$

I'm sorry, I don't know how to put latex code.

Answer 1

Because if $a=-1$ then $a^2=(-1)^2\neq -(1^2)$. Yo are treating $a^2=-(1^2)$, which is wrong.

Answer 2

You are wrong here.

$a^{p} b^{p}=(ab)^{p}$

And your math on that example is wrong. You forgot the brackets.

$(-1)^2(3)^2=(-3)^2=+9$.

Hope this helps