Which expression is equivalent to start fraction, 2, to the power 4 , divided by, left parenthesis, 2, to the power minus 6 , right parenthesis, to the power minus 1 , end fraction, question mark

Question

(2
−6
)
−1

2
4

​
?
Answer
Multiple Choice Answers
2, squared2
2

2, to the power minus 22
−2

2, to the power 102
10

2, to the power minus 42
−4

Answer 1

To simplify the expression

\[ \frac{2^4}{(2^{-6})^{-1}}, \]

we start with the denominator \((2^{-6})^{-1}\). We can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\). Thus,

\[ (2^{-6})^{-1} = 2^{-6 \cdot (-1)} = 2^6. \]

Now, substitute \(2^6\) back into the expression:

\[ \frac{2^4}{2^6}. \]

Next, we can use the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\):

\[ \frac{2^4}{2^6} = 2^{4-6} = 2^{-2}. \]

Now we have simplified the original expression to \(2^{-2}\).

Looking at the multiple-choice answers, the equivalent expression is:

\[ 2^{-2}. \]

So, the answer is:

2, to the power minus 2 (-2).