Quandaries
and Queries 

Name: Amy Who is asking: Student Level of the question: All Question: My teacher gave me the problem (2^{6}) 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? 

Amy, if it was (2^{6}) then you were right but if the question was (2)^{6} then it means ((1)^{6})(2^{6}) = (1)(64) = 64. Another way to see this is that
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Penny Hi there, If the question was written exactly like you showed (2^{6}), 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. (2^{6}) does not need the brackets and means the same as 2^{6}. This follows from the way we perform mathematical operations. We do exponentiation before addition or subtraction. 2^{6} = 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. Leeanne
