E. 1 Prime factorization 46 F Write the prime factorization of 500 . Use exponents when appropriate and order the factors from least to greatest (for example, $$ 2^{2} \cdot 3 \cdot 5 $$ ).

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To find the prime factorization of $$ 500 $$, we will follow these steps:

1. **Divide by the smallest prime number**: Start with the smallest prime number, which is $$ 2 $$, and divide $$ 500 $$ by $$ 2 $$ until it is no longer divisible by $$ 2 $$.

2. **Continue with the next prime numbers**: Once $$ 500 $$ is no longer divisible by $$ 2 $$, move to the next smallest prime number, which is $$ 3 $$, and repeat the process. Continue this with $$ 5 $$, $$ 7 $$, etc., until the quotient is $$ 1 $$.

Let's perform the factorization step by step:

- $$ 500 \div 2 = 250 $$
- $$ 250 \div 2 = 125 $$ (now $$ 125 $$ is not divisible by $$ 2 $$)
- $$ 125 \div 5 = 25 $$
- $$ 25 \div 5 = 5 $$
- $$ 5 \div 5 = 1 $$

Now, we can summarize the prime factors we found:

- $$ 2 $$ appears $$ 2 $$ times (from $$ 500 $$ to $$ 250 $$ to $$ 125 $$).
- $$ 5 $$ appears $$ 3 $$ times (from $$ 125 $$ to $$ 25 $$ to $$ 5 $$).

Thus, the prime factorization of $$ 500 $$ is:

$$
2^{2} \cdot 5^{3}
$$

So, the final answer is:

$$
2^{2} \cdot 5^{3}
$$
The prime factorization of 500 is $$ 2^{2} \cdot 5^{3} $$.

E. 1 Prime factorization 46 F Write the prime factorization of 500 . Use exponents when appropriate and order the factors from least to greatest (for example, \( 2^{2} \cdot 3 \cdot 5 \) ).

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