To multiply the given numbers and express the result in scientific notation, follow these steps:

1. Multiply the coefficients: $8.4 \times 1.1 = 9.24$

2. Add the exponents (since both numbers are in scientific notation and being multiplied): $10^7 \times 10^6 = 10^{7+6} = 10^{13}$

3. Combine the results: $9.24 \times 10^{13}$

So, the product is: $\boxed{9.24 \times 10^{13}}$

Would you like more details or have any questions about this process?

Here are 5 related questions for practice:

1. Multiply $(3.2 \times 10^5) \times (4.7 \times 10^3)$.
2. How would you express $(5.1 \times 10^8) \times (2.0 \times 10^{-4})$ in scientific notation?
3. Divide $(6.3 \times 10^{9}) \div (2.1 \times 10^4)$.
4. What is the sum of $(2.8 \times 10^6)$ and $(1.4 \times 10^7)$?
5. Simplify $(7.0 \times 10^3)^2$ in scientific notation.

Tip: When multiplying in scientific notation, always remember to multiply the coefficients first, then handle the exponents separately!