Question
Which expression is equivalent to start fraction, 2, to the power minus 6 , divided by, 2, to the power minus 8 , times, 2, to the power minus 7 , end fraction, question mark
2
−8
×2
−7
2
−6
?
Answer
Multiple Choice Answers
2, to the power 102
10
2, to the power 112
11
2, to the power 212
21
2, to the power 92
9
2
−8
×2
−7
2
−6
?
Answer
Multiple Choice Answers
2, to the power 102
10
2, to the power 112
11
2, to the power 212
21
2, to the power 92
9
Answers
GPT-4o mini
To simplify the expression \(\frac{2^{-6}}{2^{-8} \times 2^{-7}}\), we can use the properties of exponents.
First, let's simplify the denominator:
1. **Denominator:**
\[
2^{-8} \times 2^{-7} = 2^{-8 + (-7)} = 2^{-8 - 7} = 2^{-15}
\]
2. **Putting it all together:**
Now we can rewrite the entire expression:
\[
\frac{2^{-6}}{2^{-15}}
\]
3. **Using the property of exponents** (\(a^m / a^n = a^{m-n}\)):
\[
= 2^{-6 - (-15)} = 2^{-6 + 15} = 2^{9}
\]
Thus, the expression simplifies to \(2^{9}\).
**Final Answer:**
The correct answer from the multiple-choice options is:
\[
2^{9}
\]
First, let's simplify the denominator:
1. **Denominator:**
\[
2^{-8} \times 2^{-7} = 2^{-8 + (-7)} = 2^{-8 - 7} = 2^{-15}
\]
2. **Putting it all together:**
Now we can rewrite the entire expression:
\[
\frac{2^{-6}}{2^{-15}}
\]
3. **Using the property of exponents** (\(a^m / a^n = a^{m-n}\)):
\[
= 2^{-6 - (-15)} = 2^{-6 + 15} = 2^{9}
\]
Thus, the expression simplifies to \(2^{9}\).
**Final Answer:**
The correct answer from the multiple-choice options is:
\[
2^{9}
\]