1 answer
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John's error is assuming that any number to the zero power (except 0^0) equals 1. In this case, the base is 2, not 0.
Carol's error is confusing the rules of exponentiation. When multiplying with the same base, the exponents should be added, not multiplied.
To find the correct answer, let's simplify the expression step by step:
(2^2 x 2^-6)^-3 x 2^0
= (4 x 1/64)^-3 x 1
= (4/64)^-3
= (1/16)^-3
= (1 / (1/16)^3)
= 1 / (1 / 4096)
= 4096
So, the correct answer is 4096.