To perform the prime factorization of $0.008$, we first convert the decimal into a fraction:

$0.008 = \frac{8}{1000}$

Next, simplify the fraction:

$\frac{8}{1000} = \frac{8 \div 8}{1000 \div 8} = \frac{1}{125}$

Now, factor $125$:

$125 = 5^3$

Thus:

$\frac{1}{125} = \frac{1}{5^3}$

Therefore, the prime factorization of $0.008$ is:

$\frac{1}{5^3}$

This means that $0.008$ is equivalent to $1$ divided by $5^3$.

Would you like more details or have any questions?

Here are five related questions to explore:

1. How do you find the prime factorization of larger decimals?
2. What is the prime factorization of $125$?
3. How do you express other fractions in terms of prime factors?
4. How does prime factorization help simplify fractions?
5. What is the prime factorization of $1000$?

Tip: Always start by converting decimals to fractions when doing prime factorizations.