Question

Rewrite the expression as a product of identical factors to find the product for 10032
. Submit your answer in simplified form.



(1 point)
Remaining Attempts : 3

Answer 1

thats wrong

Answer 2

To express the number 10032 as a product of identical factors, we can start by finding its prime factorization and then express it as a power of prime factors if applicable.

1. **Prime factorization of 10032**:

- 10032 is even, so we begin by dividing by 2:
- \(10032 \div 2 = 5016\)
- \(5016 \div 2 = 2508\)
- \(2508 \div 2 = 1254\)
- \(1254 \div 2 = 627\)

627 is not divisible by 2. Next, we check for divisibility by 3:
- \(627 \div 3 = 209\)

Now, we check for divisibility of 209. It is not divisible by 3, nor by 5. Checking for 11, we find:
- \(209 \div 11 = 19\) (both 11 and 19 are primes).

Putting it all together, we have:
\[
10032 = 2^4 \times 3^1 \times 11^1 \times 19^1
\]

2. **Expressing the product**:
We can use the powers of prime factors to express 10032 as a product of identical factors. The lowest power in the prime factorization is \(3^1, 11^1, 19^1\). Since there is no identical factor in the base forms, we can express it in a different way:

To simplify, we find how we can express this using a perfect square or cube. Since the greatest power of 2 is 4, we can express 10032 using pairs of the same factor.

\[
10032 = (2^2 \cdot 3 \cdot 11 \cdot 19) \cdot 4 = (4 \cdot 3 \cdot 11 \cdot 19) \cdot 4 = 76 \cdot 4
\]

Calculating \(76 \cdot 4\):
\[
76 = 4 \cdot 19
\]

Finally:
\[
10032 = (4 \cdot 19) \cdot (4 \cdot 19)
\]

Thus, we can rewrite 10032 as:
\[
(4 \times 19 \times 2) \times (4 \times 19 \times 2) = (76) \times (76) = 76^2
\]

Conclusively, the simplified expression for 10032 expressed as a product of identical factors is:
\[
\boxed{76^2}
\]