1. The problem asks for the exponential form of the product $108 \times 192$. 2. To express a number in exponential form, we first find its prime factorization. 3. Let's start with $108$: $$108 = 2 \times 54 = 2 \times 2 \times 27 = 2^2 \times 3^3$$ 4. Now for $192$: $$192 = 2 \times 96 = 2 \times 2 \times 48 = 2^2 \times 48 = 2^2 \times 2 \times 24 = 2^3 \times 24 = 2^3 \times 2 \times 12 = 2^4 \times 12 = 2^4 \times 2 \times 6 = 2^5 \times 6 = 2^5 \times 2 \times 3 = 2^6 \times 3$$ 5. Now multiply the two numbers in their prime factorization form: $$108 \times 192 = (2^2 \times 3^3) \times (2^6 \times 3) = 2^{2+6} \times 3^{3+1} = 2^8 \times 3^4$$ 6. Therefore, the exponential form of $108 \times 192$ is: $$\boxed{2^8 \times 3^4}$$ This means the product can be expressed as $2$ raised to the power $8$ multiplied by $3$ raised to the power $4$.