Question

Rational Exponents Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
1 of 51 of 5 Items
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 : 2

Answer 1

im lost what is the answer

Answer 2

To rewrite the expression \( 10032 \) as a product of identical factors, we first need to break it down using prime factorization.

Let's find the prime factorization of \( 10032 \):

1. Since \( 10032 \) is even, divide by \( 2 \):
\[
10032 \div 2 = 5016
\]

2. Continuing to divide by \( 2 \):
\[
5016 \div 2 = 2508
\]
\[
2508 \div 2 = 1254
\]
\[
1254 \div 2 = 627
\]

3. Now \( 627 \) is not even, so let's try dividing by \( 3 \):
\[
627 \div 3 = 209
\]

4. Next, check \( 209 \). It is not divisible by \( 3 \) (the sum of digits \( 2 + 0 + 9 = 11 \) does not divide by \( 3 \)). Check divisibility by \( 11 \):
\[
209 \div 11 = 19
\]

5. Now \( 19 \) is prime.

So, the complete prime factorization of \( 10032 \) is:
\[
10032 = 2^4 \cdot 3^1 \cdot 11^1 \cdot 19^1
\]

Now, we can express \( 10032 \) as a product of identical factors:

\[
10032 = (2^4) \cdot (3^1) \cdot (11^1) \cdot (19^1)
\]

If we simplify it to use the smallest individual factors:
\[
10032 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 11 \cdot 19
\]

Hence, in simplified form, you can write the product as:
\[
(2^4) \cdot 3 \cdot 11 \cdot 19
\]

You can also express all identical factors for the exponent:
\[
10032 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 11 \cdot 19
\]

If an exact formatted answer is needed:
\[
10032 = 2^4 \cdot 3^1 \cdot 11^1 \cdot 19^1
\]

That can also be written in simple terms:
\[
2^4 \cdot 3 \cdot 11 \cdot 19
\]

This representation shows \( 10032 \) as a product of its identical factors, each represented by its prime factorization.