Which expressions are equivalent to (2^5)^-2 a) 2^-10 and 1/20 b) 2^-10 and 1/1024 c) 10^-2 and 1/100 d) 10^-10 and 1/100

Choice B) 2^(-10) and 1/1024



Explanation:

We'll use these two rules
Rule 1: (a^b)^c = a^(b*c)
Rule 2: a^(-b) = 1/(a^b)

Using rule 1 above, we can say
(2^5)^(-2) = 2^(5*(-2)) = 2^(-10)
So 2^(-10) is one of the answers

Now use rule 2 to convert 2^(-10) into...
2^(-10) = 1/(2^10) = 1/1024
so 1/1024 is the other answer