Question

PLEASE HELP !!! I NEED THE ANSWER IN THE NEXT HOUR

Answer 1

This is not a prime factorization.

The correct prime factorization is
`2^5*3*5^4*11^2`

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Further Explanation:

The expression your teacher gave you is not a prime factorization because the 8 isn't prime.

8 = 2*2*2 =
`2^3`

If we replace 8 with
`2^3`, then we go from

`2^2*3*5^4*8*11^2`

to

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

and that rearranges to

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

Then we can simplify the
`2^2*2^3` portion to get
`2^5` since we add the exponents while keeping the base '2' the same.

We therefore end up with

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

as the correct prime factorization. Each base (2,3,5,11) is a prime number.

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As a check, use your calculator to type in

2^2*3*5^4*8*11^2

and also

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

and you should get the result of 7,260,000 each time. Since we get the same result, this confirms 2^2*3*5^4*8*11^2 = 2^5*3*5^4*11^2