Which expression is equivalent to start fraction, 2, squared, divided by, 2, to the power minus 7 , end fraction, times, 2, question mark

Question

2
−7

2
2

​
×2?
Answer
Multiple Choice Answers
2, to the power 122
12

2, to the power 82
8

2, to the power 92
9

2, to the power 102
10

Answer 1

To simplify the given expression \(\frac{2^2}{2^{-7}} \times 2\), we can start by simplifying the fraction:

1. Simplifying the Fraction: When we divide powers with the same base, we subtract the exponents. So,

\[ \frac{2^2}{2^{-7}} = 2^{2 - (-7)} = 2^{2 + 7} = 2^9. \]

2. Multiplying by \(2\): Now, we multiply \(2^9\) by \(2\). We can write \(2\) as \(2^1\):

\[ 2^9 \times 2^1 = 2^{9 + 1} = 2^{10}. \]

Therefore, the expression simplifies to \(2^{10}\).

So the answer is \(2^{10}\).

Correct Answer: \(2, \text{ to the power } 10\).