Calculate the product below and give your answer in scientific notation.

To find the product \( \left(8 \times 10^{-3}\right) \times \left(0.0002\right) \), we can first express \(0.0002\) in scientific notation.

We know that: \[ 0.0002 = 2 \times 10^{-4} \]

Now we can substitute this into our problem: \[ \left(8 \times 10^{-3}\right) \times \left(2 \times 10^{-4}\right) \]

Next, we can rearrange the expression using the associative and commutative properties of multiplication: \[ (8 \times 2) \times (10^{-3} \times 10^{-4}) \]

Calculating \(8 \times 2\): \[ 8 \times 2 = 16 \]

Now we can handle the powers of ten: \[ 10^{-3} \times 10^{-4} = 10^{-3 + (-4)} = 10^{-7} \]

Putting it all together: \[ 16 \times 10^{-7} \]

Finally, to express \(16\) in scientific notation, we can write it as \(1.6 \times 10^1\): \[ 16 \times 10^{-7} = 1.6 \times 10^1 \times 10^{-7} = 1.6 \times 10^{1 - 7} = 1.6 \times 10^{-6} \]

So, the final answer in scientific notation is: \[ \boxed{1.6 \times 10^{-6}} \]