Let's simplify the expression $10^{-6} \times 10^{-4} \times 10^{3}$.

When multiplying powers of 10, you add the exponents:

$10^{-6} \times 10^{-4} \times 10^{3} = 10^{-6 + (-4) + 3}$

Simplifying the exponents:

$-6 - 4 + 3 = -7$

So the expression becomes:

$10^{-7}$

Therefore, the simplified result is $10^{-7}$.

Let me know if you need any further details or have more questions!

Here are some related questions:

1. How would this change if the exponents were positive?
2. What is the general rule for multiplying numbers with the same base in exponent notation?
3. How do you handle division when using exponents?
4. What is the value of $10^{-7}$ as a decimal?
5. Can this rule be applied to other bases, like 2 or 5?

Tip: When multiplying powers of the same base, just add the exponents!