The product $0.08\times 0.0052$ is equal to:

Let's convert both numbers into scientific notation format:
$$0.08=8\times 10^{-2}$$

$$0.0052=52\times 10^{-4}$$

Multiply the terms:

$$(8\times 10^{-2})\times (52\times 10^{-4})=(8\times 52)\times 10^{-2+(-4)}$$

$$=416\times 10^{-6}$$

Converting $416$ to standard scientific notation ($4.16\times 10^2$):

$$=4.16\times 10^2\times 10^{-6}=4.16\times 10^{-4}$$