In the diagram below, the shortest paths from A to B along the gridlines are 6 units long. How many of these paths are there?
Solution to yesterday’s problem:
The trick here is that all of the exponents have two as a base. So we have to find a way to take out all the bases and leave only the exponents in our equation. Here’s the equation again:
Recall that when you divide two exponents with the same base, the result is the base taken to the difference of the two exponents. For example, . Here, we can subtract the two exponents as well:
So our new equation is
In order for the two sides of this equation to be equal, both exponents have to be equal. So here’s where we take out the bases:
So n = -1.