Question

(6a^-4b^2)^-2 for the ^ it is an exponent,

Answer 1

Negative exponents work the same as positive ones, except you have to consider the inverse of the base.

So, if for example $4^3 = 64$, in the same fashion you have

$4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{64}$

So, negative exponents lead to a fraction with numerator 1 and denominator the same expression, but with positive exponent.

So, in your case, let's work with the inner parenthesis first:

$6a^{-4}b^2 = 6 \dfrac{1}{a^4}b^2 = \dfrac{6b^2}{a^4}$

Now, if we want to raise this to the negative two, we have

$\left(\dfrac{6b^2}{a^4}\right)^{-2} = \dfrac{1}{\left(\frac{6b^2}{a^4}\right)^2}} = \dfrac{1}{\frac{36b^4}{a^8}} = \dfrac{a^8}{36b^4}$