The two equations connecting m and n are: 2^m imes 3ⁿ = 212 and 3^m imes 3ⁿ = 9. Find the values of m and n.

Step 1: Write down the two equations connecting $m$ and $n$.
The first given equation is:

$$2^m \times 3^n = 212 \quad (1)$$

The second given equation is:

$$3^m \times 3^n = 9$$

Using the exponent rule $a^x \times a^y = a^{x+y}$, we can simplify the second equation:

$$3^{m+n} = 3^2$$

Equating the exponents, we get the second equation:

$$m+n = 2 \quad (2)$$

The two equations connecting $m$ and $n$ are:
$\boxed{2^