I am fully convinced now.We have explained this to you repeatedly, such as what I said here:
It is not something to prove mathematically, but a standard convention, that when we write something like [imath]-x^y[/imath] the exponent applies only to [imath]x[/imath], not to [imath]-x[/imath]. For evidence, consider these sources:
Demonstrates how to use exponents on negative numbers. Points out the difference that parentheses can make, and warns against a common mistake.www.purplemath.com
Some of these mention that some calculators or programs follow a different rule, but the mathematical rule is as we say.
So your thinking is wrong. Rather than your [math]-2^6=(-2)^6=(-2)(-2)(-2)(-2)(-2)(-2)=64[/math]the reality is [math]-2^6=-(2^6)=-(2)(2)(2)(2)(2)(2)=-64[/math]