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 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 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.