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

Question

4
−1

(4
−2
)
−1

​
?
Answer
Multiple Choice Answers
start fraction, 1, divided by, 16, end fraction
16
1
​

one quarter
4
1
​

6464
start fraction, 1, divided by, 64, end fraction
64
1
​

Answer 1

The expression you provided is \(\frac{(4^{-2})^{-1}}{4^{-1}}\).

Let's simplify it step by step.

1. Simplify \((4^{-2})^{-1}\): \[ (4^{-2})^{-1} = 4^{2} = 16 \]

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

3. Now substitute back into the expression: \[ \frac{16}{4} \]

4. Finally simplify \(\frac{16}{4}\): \[ \frac{16}{4} = 4 \]

So the expression simplifies to \(4\).

Therefore, the correct answer is: \[ \boxed{4} \]