Question

Apply the Quotient Rule of Exponents to form an equivalent expression of 2622
.(1 point)
Responses

212
2 superscript 12 baseline

23
2 cubed

28
2 superscript 8 baseline

24

Answer 1

To apply the Quotient Rule of Exponents, we first rewrite the expression \( 2622 \) using its prime factorization.

Now let's decompose \( 2622 \):

1. Start by factoring \( 2622 \):
- \( 2622 \) is even, so divide by \( 2 \):
\[
2622 \div 2 = 1311
\]
- Now, factor \( 1311 \). Check divisibility by \( 3 \) (sum of digits: \( 1 + 3 + 1 + 1 = 6 \) is divisible by \( 3 \)):
\[
1311 \div 3 = 437
\]
- Now factor \( 437 \). Check divisibility by prime numbers:
- It is not divisible by \( 2 \), \( 3 \), \( 5 \).
- Check \( 7 \) and so on until \( 19 \):
\[
437 \div 19 = 23
\]
- So we have factored \( 437 = 19 \times 23 \).

Thus, the complete factorization of \( 2622 \) is:
\[
2622 = 2^1 \times 3^1 \times 19^1 \times 23^1
\]

Next, let's express it as a power of \( 2 \) only. From the context given and the response options, we need to find a power of \( 2 \) equivalent to \( 2622 \).

Since none of the given options directly relates to the factorization, it appears there was a misinterpretation of applying the Quotient Rule directly to find a power representation from base \( 2 \).

Given that the expression \( 2622 \) does not fit neatly into a single power of \( 2 \), the provided options likely involve some additional context (like further simplification or theoretical consideration). Provided are:

1. \( 2^{12} \)
2. \( 2^3 \)
3. \( 2^8 \)
4. \( 2^4 \)

To find if somehow one of these may be relevant in related forms or games of the Quotient Rule:

- \( 2^{12} \) does not fit.
- \( 2^3 = 8 \) meaning \( 2^3 \times k\) where k doesn't make \( 2622 \).
- Similarly, for \( 2^4, 2^8 \) would deviate.

Therefore, without deeper context for transforming to these values, we conclude we need to lean into what \( 2622 \) factors provide and return the basic observation from \( 2 \).

So overall, please confirm the query format and context, or verify which \( k \) factorial grouping to align with the Quotient Rule—to redefine \( 2622 \) under the base \( 2 \) or if through cumulative approach for another answer.

None of the provided expressions directly correspond to \( 2622 \).