We are given the expression:

$10^{\log_{10}3 + \log_{10}2}$

We can simplify it step by step:

1. Use the logarithmic property: The sum of logarithms with the same base is equal to the logarithm of the product of their arguments:

   $\log_{10}3 + \log_{10}2 = \log_{10}(3 \times 2) = \log_{10}6$

2. Now, the expression becomes:

   $10^{\log_{10}6}$

3. Apply the property $10^{\log_{10}x} = x$:

   $10^{\log_{10}6} = 6$

Thus, the value of the expression is:

$6$

Would you like any further explanation on logarithmic properties?

Here are some related questions you might find interesting:

1. What is the relationship between logarithms and exponents?
2. How do logarithmic and exponential functions interact in algebra?
3. What is the change of base formula for logarithms?
4. How do you solve equations involving logarithms?
5. How can you simplify logarithmic expressions with different bases?

Tip: Remember, simplifying logarithms often relies on recognizing basic properties like the product, quotient, and power rules!