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 
2 
2
 
(2 
−1
 ) 
4
 
​
 ?

Let's break down the given expression step by step. The expression is:

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

### Step 1: Simplify \((2^{-1})^4\)
When raising a power to another power, you multiply the exponents. Therefore:

\[
(2^{-1})^4 = 2^{-1 \times 4} = 2^{-4}
\]

So now the expression becomes:

\[
\frac{2^{-4}}{2^2}
\]

### Step 2: Apply the quotient rule for exponents
The quotient rule states that when dividing like bases, you subtract the exponents:

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

### Step 3: Simplify the result
The expression \(2^{-6}\) can be written as:

\[
2^{-6} = \frac{1}{2^6} = \frac{1}{64}
\]

### Final Answer:
The expression is equivalent to \(\frac{1}{64}\).

Would you like further details or clarifications? Here are some related questions:

1. What is the power of a power rule?
2. How do you handle negative exponents?
3. Can you explain the quotient rule for exponents?
4. What happens if you raise a negative exponent to another power?
5. How can I convert negative exponents to fractions?

**Tip:** When working with negative exponents, remember they represent the reciprocal of the base raised to the positive exponent.

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?

Learn how to simplify the expression (2^(-1))^4 ÷ 2^2 using exponentiation rules, including the power of a power rule, the quotient rule, and negative exponents. This step-by-step guide is ideal for students in Grades 8-10.

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