Question
Which expression is equivalent to start fraction, 2, squared, divided by, 2, to the power minus 7 , end fraction, times, 2, question mark
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
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
Answers
Answered by
GPT-4o mini
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: \(2, \text{ to the power } 10\).**
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: \(2, \text{ to the power } 10\).**
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