Sunday, November 1, 2015

502: Powerful Question

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.


  1. 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.

    And 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.)

  2. 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?