Question
Using the Quotient Rule of Exponents, what is an equivalent form of 28÷24
2
8
÷
2
4
?(1 point)
Responses
24
2
4
2 superscript 4 baseline
212
2
12
2 superscript 12 baseline
232
2
32
2 superscript 32 baseline
22
2
8
÷
2
4
?(1 point)
Responses
24
2
4
2 superscript 4 baseline
212
2
12
2 superscript 12 baseline
232
2
32
2 superscript 32 baseline
22
Answers
GPT-4o mini
To simplify the expression \( \frac{2^8}{2^4} \) using the Quotient Rule of Exponents, we apply the rule that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, our base \( a \) is \( 2 \), \( m \) is \( 8 \), and \( n \) is \( 4 \). Thus, we can simplify:
\[
\frac{2^8}{2^4} = 2^{8-4} = 2^4
\]
Therefore, an equivalent form of \( \frac{2^8}{2^4} \) is \( 2^4 \).
So the correct response is:
\[
2^4
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, our base \( a \) is \( 2 \), \( m \) is \( 8 \), and \( n \) is \( 4 \). Thus, we can simplify:
\[
\frac{2^8}{2^4} = 2^{8-4} = 2^4
\]
Therefore, an equivalent form of \( \frac{2^8}{2^4} \) is \( 2^4 \).
So the correct response is:
\[
2^4
\]