Which expression is equivalent to left parenthesis, start fraction, 2, to the power minus 1 , divided by, 2, to the power 0 , end fraction, right parenthesis, to the power minus 2 , question mark(

Question

2
0

2
−1

​
)
−2
?
Answer
Multiple Choice Answers
00
one quarter
4
1
​

one eigth
8
1
​

44

Answer 1

To simplify the expression \(\left(\frac{2^{-1}}{2^{0}}\right)^{-2}\), we can follow these steps:

1. Simplify the fraction inside the parentheses:
   Since \(2^{0} = 1\), we can simplify the fraction: \[ \frac{2^{-1}}{2^{0}} = \frac{2^{-1}}{1} = 2^{-1} \]

2. Now the expression becomes: \[ \left(2^{-1}\right)^{-2} \]

3. Apply the exponent: Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify: \[ \left(2^{-1}\right)^{-2} = 2^{-1 \cdot (-2)} = 2^{2} = 4 \]

Therefore, the equivalent expression is 4.

So the answer is 4.