Quandaries and Queries
Who is asking: Student
Level of the question: All
Question: My teacher gave me the problem (-26) on our homework. She marked it wrong when I wrote down -64 for an answer. She said the correct answer was 64. Can you explain why it is 64?
if it was -(26) then you were right but if the question was (-2)6 then it means ((-1)6)(26) = (1)(64) = 64.
Another way to see this is that
If the question was written exactly like you showed (-26), then you are correct and the answer should have been -64.
However, if the question was actually (-2)6, then your teacher is correct and the answer is 64. The placement of the brackets is critical in situations where there are negative signs with exponents.
Ex. (-26) does not need the brackets and means the same as -26. This follows from the way we perform mathematical operations. We do exponentiation before addition or subtraction.
-26 = -1 x 2 x 2 x 2 x 2 x 2 x 2 = -64
(-2)6 = (-2)(-2)(-2)(-2)(-2)(-2) = 64
Hope this helps.