The Product Rule of Exponents states that when multiplying two powers with the same base, you can add the exponents. In the case of the expression \(19 \cdot 18\), both 19 and 18 are not powers, but if we treat them as powers of a base, we could express them as follows:
Assuming we consider \(19 = 19^1\) and \(18 = 18^1\), we find: \[ 19 \cdot 18 = 19^1 \cdot 18^1 \]
However, since we want to express the product \(19 \cdot 18\) using exponents of a common base, we don't have an obvious way to simplify them using the Product Rule without introducing a new base.
Thus, treating them in the context of exponentiation directly doesn't yield a standard product representation with the same base. If you specifically seek that representation, you would need to define a common base or find a way to express both numbers as powers.
If we presume \( a = 19 \) and express \( b = 18 \) directly, the formula could be: \[ 19 \cdot 18 = (base)^{(exponent)} \] where \( base \) does not have a single common base representation derived from the original numbers.
The answer remains:
- base = 19, 18
- exponent = 1
In conclusion, simply state that \( 19 \cdot 18 \) is already the product of two distinct integers rather than a power of a single base.