Question

Using the Quotient Rule of Exponents, what is an equivalent form of 28÷24 ?(1 point) Responses 212 2 superscript 12 baseline 232 2 superscript 32 baseline 22

Answer 1

To simplify \( 28 \div 24 \) using the Quotient Rule of Exponents, we can express the numbers using exponents.

We know that:

- \( 28 = 2^4 \times 7 \)
- \( 24 = 2^3 \times 3 \)

So we rewrite the division as follows:

\[
\frac{28}{24} = \frac{2^4 \times 7}{2^3 \times 3}
\]

Using the Quotient Rule of Exponents \( \frac{a^m}{a^n} = a^{m-n} \):

\[
\frac{2^4}{2^3} = 2^{4-3} = 2^1
\]

Thus, we can simplify our expression to:

\[
\frac{28}{24} = 2^1 \times \frac{7}{3}
\]

However, if we're only looking for the equivalent exponent form, the term \( \frac{28}{24} \) simplifies primarily to \( 2^1 \) when focused on the powers of 2 involved.

Among the response options provided, the closest match to \( 2^1 \) is:

\( 2^2 \)

So an equivalent form of \( \frac{28}{24} \) in exponent form is \( 2^1 \), but since that option might not be visible depending on what exactly was provided in your list, it seems that the answer \( 2^2 \) that you needed might not directly correspond to \( \frac{28}{24} \) simplistically as it actually leads us to list other forms.

Ultimately, based on your list I recommend going for the answer that lies closest to what would apply typically, the form \( 2^2 \).