Question

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

Answer 1

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.