Gary has his function$g\left(x\right) = 10^{x}$ and Amy has her function$a\left(m\right) = 10^{m}$ .

1. Each person is going to choose a whole number at random from the numbers $1$, $2$, $3$…$10$, and substitute it into his or her respective function. After they do this, what is the probability that $g\left(x\right) = a\left(m\right)$?

   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 $g\left(x\right)\cdot a\left(m\right)$.

   Hint (b):

   Remember the exponent rules.

   Answer (b):

   $10^{x + m}$