It's not included in the PEMDAS Order of Operations ...
Should $a^{b^c} = ({a^b})^c$ or should it be $a^{b^c} = a^{(b^c)}$ ??
Does $3^{2^0}$ equal 1 or 3?
Let's just consider easy numbers {1, 2, 3, 4} so we can explore. What's the probability that the two methods arrive at the same answer?
For the record, $a^{b^c} = a^{(b^c)}$ is the accepted order of operations here.
Strictly speaking, $20 \div 10 \div 2$ is "not included in the PEMDAS order of operations" either. (Is it $1$ or $4$?) The takeaway is that, when we lose associativity, parentheses can be necessary in making an expression unambiguous.
ReplyDeleteAnd so, while there may exist an accepted order of operations for a tower of exponents, it would be best to use parentheses from the outset...
(For the actual question posed: It is not clear to me whether the numbers can be picked with repetition. Is a=b=c=2 a possibility? Etc.)
Choose whichever suits your students' whim. I say, sure a=b=c=2 is fine, making 64 different ways to pick the numbers. If you'd rather, do it the other way. These questions are meant to spark discussion. Maybe leave it up to the kids?
ReplyDelete