Question

Can someone help me with this please?

Answer 1

9514 1404 393

Answer:

see below

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)

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`(-2^2)^(-6)/(2^(-5))^(-4)=2^(-12)/2^(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}`

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Please note that ...

`(-2^2)^(-6)=(1)/((-4)^6)=(1)/(4096)=2^(-12)`

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.