Which expression is equivalent to start fraction, left parenthesis, 2, to the power minus 1 , right parenthesis, to the power 4 , divided by, 2, squared, end fraction, question mark

Question

2
2

(2
−1
)
4

​
?
Answer
Multiple Choice Answers
2, squared2
2

2, to the power minus 22
−2

2, to the power minus 82
−8

2, to the power minus 62
−6

Answer 1

To simplify the expression \(\frac{(2^{-1})^4}{2^2}\), we can start by simplifying the numerator.

1. Simplify the numerator: \[ (2^{-1})^4 = 2^{-1 \cdot 4} = 2^{-4} \]

2. Now rewrite the expression: \[ \frac{2^{-4}}{2^2} \]

3. Use the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\): \[ \frac{2^{-4}}{2^2} = 2^{-4 - 2} = 2^{-6} \]

Therefore, the equivalent expression is \(2^{-6}\).

The correct answer is: \[ \text{2, to the power minus 6} \quad (2^{-6}) \]