The correct answer is 2^-3.
Using f(a^m)^n = a^(mn), the exponential identity
(2^-1)^3 = 2^-3
The symbol indicating organisms A's
Population decline during the following three days is (1/2)^3.
This can be written as (2-^1)3 with the same base but one exponent. hence answer is 2^-3. Proof of of identity is given below
case 1 Let m>0 and n>0 in . We'll move forward via induction. We repair m and introduce n. Basis: Assume that n=1. Am Equals Am, as can be seen. logical inference: Let's say (am)k=amk. We will demonstrate that (am)k+1=am(k+1). The assumption that (am)k+1=am(k+1) follows naturally.
Case 2 M=N=0 in . There is no doubt that (am)n=amn.
case 3: m0 and n0. Let t, r > 0 and m = t and n = r. Consequently, (a^m)^n=(at)r)=(a1)t)r)=(a1)rt)=(ant)=(ant)=an(1)t=a^mn.
Learn more about (a^m)^n identity here :-
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