Why is $x^{x^x}=x^{x x}=x^{x^2}=x^{2x}$ wrong? I was solving an excercise that involved the expression:
$$x^{x^x}$$
I decided to apply property of exponentials ($a^{b^c}=a^{bc}$) And I could arrive at the following:
$$x^{x x}=x^{x^2}=x^{2x}$$
But this is clearly wrong, I want to know why is it incorrectly, since it just seems as normal use of exponent laws

Numeric examples are good to provide a check on which expressions are equal.  Consider
$$2^{3^2}.$$
Thinking of this as $2^{(3^2)}$ gives $2^{3^2} = 2^9 = 512$.  That's not the same as $2^{3\cdot2} = 2^6 = 64$ (which is the same as $(2^3)^2 = 8^2 = 64$).
So $a^{b^c} = a^{bc}$ is not a valid property of exponents.
