Question

A number is written using the following factorization: 2² x 3 x 5⁴ x 8 x 11². Is this factorization a prime factorization? Explain why of why not. If it is not correct, give the correct prime factorization of the number.

Answer 1

I need help fast!!!!!

Answer 2

In a prime factorization we write the number as a product of powers of primes
Here we are given the prime factorization as-\(2^2 \times 3 \times 5^4 \times 8 \times 11^2\)
it will not be considered as prime factorization because it has \(\color{red}{8}\) which is not a prime
To write to correct prime factorization we just need to convert \(8\) into its prime factorization form
prime factorization of \(8\) is -->\(2 \times 2 \times 2=2^3\)

so just replace \(8\) with \(2^3\) in the expression

we had this->\(2^2 \times 3 \times 5^4 \times 8 \times 11^2\)

after replacing \(8\) with \(2^3\) we get this-
prime factorization-->\(2^2 \times 3 \times 5^4 \times 2^3 \times 11^2\)

we can simplify it to this-
prime factorization--->\(2^5 \times 3 \times 5^4 \times 11^2\)