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.