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.
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
1 answer
1 answer