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

Question

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

Answer 1

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: \[ 2^{9} \]