what is the easiest way to remember the order of operations over a lifetime.
What different rule when working out exponents any feedback ?
Wikipedia gives a comprehensive overview of the rules of working with exponents: Exponentiation - Wikipedia, the free encyclopedia
And most of these are fairly intuitive. For example is equivalent to multiplying by itself m times and then dividing by n times, resulting in . Or for instance .
How do YOU keep the rules of exponents straight ?
When I was first learning these Rules, I came up with a "picture" of what was happening.
It was quite primitive (and even childish), but it worked for me.
Think of the "heirarchy" of some basic operations.
First we learned to Count objects: .
Then came Addition, which is "repeated counting."
. . (and Subtraction is "repeated take-away.")
Then came Multiplication, which is "repeated addition."
. . (and Division is "repeated subtraction.")
Finally, we learned Powers, which is "repeated multiplication."
. . (and Roots are "repeated division.")
So, written in order, we have:
With the Rules of Exponents, we reverse the order . . .
I really didn't visualize these diagrams.
I noted that, for exponents, we "step down" an operation.
(For example, to multiply, we add exponents . . . and so on.)