Question

Students were given the task to fully simplify
(2^2*2^-6)^-3*(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*2=4 and for the exponents 2+-6=-4 and -4*-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: John incorrectly assumed that any number raised to the power of 0 is always equal to 1. However, in this specific expression, there are other factors that need to be taken into consideration.

Carol's error: Carol mistakenly simplified 2^2 to 4 and then further simplified 2^-6 to -4. Additionally, she multiplied the exponents instead of adding them.

To find the correct answer, we need to follow the order of operations (PEMDAS).

(2^2 * 2^-6)^-3 * 2^0

First, we simplify the expression inside the parentheses:

2^2 * 2^-6 = 2^(2 + -6) = 2^-4

Next, we simplify the exponent -3 with the base 2^-4:

(2^-4)^-3

Applying the power of a power rule, we multiply the two exponents:

2^((-4) * (-3)) = 2^12

Finally, we simplify 2^0:

2^12 * 2^0 = 2^12

So, the correct answer is 2^12.