9514 1404 393
Answer:
see below
Step-by-step explanation:
The applicable properties of exponents are ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
__
[tex](-2^2)^{-6}\div(2^{-5})^{-4}=2^{-12}\div2^{20}=2^{-12-20}=\boxed{2^{-32}}\\\\2^4\cdot(2^2)^{-2}=2^{4+2(-2)}=2^0=\boxed{1}\\\\(2^2)^2\cdot (2^3)^{-3}=2^{2(2)+3(-3)}=2^{4-9}= \boxed{2^{-5}}\\\\(-2^{-4})^{-2}\cdot(2^2)^0=2^{(-4)(-2)}\cdot 1= \boxed{2^8}[/tex]
__
Please note that ...
[tex](-2^2)^{-6}=\dfrac{1}{(-4)^6}=\dfrac{1}{4096}=2^{-12}[/tex]
That is, since the outside exponent is even, the sign is immaterial. This is also true for the other expression containing -2. The result is positive.
