Could you explain this?

("Dumb it down for me")

So far I know that 2^2 x 3 x 5^4 x 8 x 11^2
is equal to 4 x 3 x 625 x 8 x 121. (I think)
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A number is written with the following factorization: 2^2 × 3 × 5^4 × 8 × 11^2. Is this factorization a prime factorization? Explain why or why not. If it is not correct, give the correct prime factorization of the number.

I don't need the answer I just need the question explained.

prime factorization:made up of primes, each to some power. In this case, 2,3,5,11 are primes, but 8 is not, it is 2^3, so prime factorization should be

2^5 * 3 *5^4 *11^2

Ah. Thank you.

do you know what the number the prime factorization is of?

To determine if the given factorization is a prime factorization, we need to check if all the factors are prime numbers, and if there are any missing prime factors.

Let's break down the given factorization:

2^2 × 3 × 5^4 × 8 × 11^2

First, let's address 8. It is not a prime number because it can be broken down into smaller factors: 2 × 2 × 2. So, we can rewrite the factorization as:

2^2 × 3 × 5^4 × 2 × 2 × 2 × 11^2

Next, let's focus on 5. The exponent of 5 is 4, which means we have four 5s multiplied together. To simplify this, we can write it as 5 × 5 × 5 × 5, which is the same as 5^4.

Now, let's sort the factors in ascending order:

2^2 × 2 × 2 × 3 × 5 × 5 × 5 × 5 × 11^2

We can see that both 2 and 5 are repeated factors. We can combine those repeated factors by multiplying them together:

2^2 × 2 × 2 × 3 × 5^4 × 11^2

Now, let's simplify the repeated factors:

2^3 × 3 × 5^4 × 11^2

This is the correct prime factorization of the number.

So, to summarize:

The given factorization, 2^2 × 3 × 5^4 × 8 × 11^2, is not a prime factorization because it includes the factor 8, which is not prime. The correct prime factorization of the number is 2^3 × 3 × 5^4 × 11^2.