Students were given the task to fully simplify: (2^2 x 2^-6)^-3 x (2)^0
John believes the answer was 1 as any number to the zero power (except 0^0 ) equals 1.
Carol believes that the answer is 4^12 since 2 x 2 = 4 and for the exponents 2 + -6 = -4 and -4 x -3 =12
What is John's error?
What is Carol's error?
What is the correct answer. Show your work.
Math
John's error is assuming that any number to the zero power equals 1. This is only true for non-zero numbers.
Carol's error is in multiplying the exponents without first simplifying the expression inside the parentheses.
To find the correct answer, we need to fully simplify the expression:
(2^2 x 2^-6)^-3 x 2^0
= (4 x 1/64)^-3 x 1
= (4/64)^-3
= (1/16)^-3
= (16)^3
= 4096
Therefore, the correct answer is 4096.