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Earlier this evening I received an SOS from my sister, who is home-schooling her two very bright young daughters. The elder daughter was solving problems in her algebra book, and came across this one:

Find [(-4)^2]^3/4 .

Young Emily multiplied two times 3/4, and got 3/2. She raised -4 to the power three, getting -64. She then took its square root, getting -8i.

Much to her consternation, the book had a different answer. They squared -4, getting 16, and eventually found 8 as the answer.

Which answer is wrong? Or is neither wrong? Why?

the parentheses/brackets force the operations to be performed in a particular sequence. Thus,

[(-4)^2]^3/4 = [16]^3/4 = 8

is the only correct solution. The text is correct.

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