The correct simplification of $(1.5 \times 10^3)(2.2 \times 10^{-3})(4.6 \times 10^{-6})$ is $1.518 \times 10^{-5}$.

This corresponds to the third option in the choices provided.

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Here are 5 related questions to explore further:

1. How do you handle multiplication of powers of 10 with different exponents?
2. What are the general rules for multiplying numbers in scientific notation?
3. How do you convert a number from scientific notation to decimal form?
4. What is the importance of significant figures in scientific notation?
5. How do you simplify products involving powers of 10?

Tip: When multiplying numbers in scientific notation, multiply the coefficients (the decimal numbers) and add the exponents of 10.