Students were given the task to fully simplify
(2^2x2^-6)^-3x(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 2x2=4 and for the exponents 2+-6=-4 and -4x -3=12
What is John's error?
What is Carol's error?
What is the correct answer. Show your work.
John's error is assuming that (2)^0 equals 1. In this case, (2)^0 actually equals 1 since anything raised to the 0 power equals 1.
Carol's error is simplifying (2^2x2^-6)^-3 incorrectly. The correct way to simplify (2^2x2^-6)^-3 is by first simplifying the exponents inside the parentheses before raising the result to the -3 power.
The correct answer can be found by simplifying the expression as follows:
(2^2x2^-6)^-3x(2)^0
= (4 x 1/64)^-3
= 4^-3 x (1/64)^-3
= 1/64^3
= 1/262144
Therefore, the correct answer is 1/262144.