Gary has his function $g(x)=10^x$ and Amy has her function $a(m)=10^m$.

1. Each person is going to choose a whole number at random from the numbers $1,2,3\dots10$, and substitute it into his or her respective function. After they do this, what is the probability that $g(x)=a(m)$?

   Hint (a):

   Notice that $g(x)$ and $a(m)$ are equivalent functions, what is the probability that Gary and Amy pick the same number?

   More Help (a):

   Assume Gary has chosen a number. How many chances does Amy have to pick the same number?
   Out of how many choices?

2. Find and simplify an expression for $g(x)·a(m)$.

   Hint (b):

   Remember the exponent rules.

   Answer (b):

   $10^{x+m}$