(2^(-1)  × 4^(-1) ) ÷ 2^(-2) = ?
	 2 	 1/2	 1/4	 4 


Let's break this down step by step:

The given expression is:

\[
\frac{2^{-1} \times 4^{-1}}{2^{-2}}
\]

### Step 1: Simplify the exponents
- \( 2^{-1} = \frac{1}{2} \)
- \( 4^{-1} = \frac{1}{4} \), and since \( 4 = 2^2 \), we can write \( 4^{-1} = (2^2)^{-1} = 2^{-2} \).
- \( 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \)

So the expression now looks like:

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

### Step 2: Multiply the terms in the numerator
\[
\frac{1}{2} \times \frac{1}{4} = \frac{1}{8}
\]

Thus, the expression becomes:

\[
\frac{\frac{1}{8}}{2^{-2}} = \frac{\frac{1}{8}}{\frac{1}{4}} 
\]

### Step 3: Divide fractions
To divide fractions, multiply the numerator by the reciprocal of the denominator:

\[
\frac{1}{8} \div \frac{1}{4} = \frac{1}{8} \times 4 = \frac{4}{8} = \frac{1}{2}
\]

### Final Answer:
\[
\boxed{\frac{1}{2}}
\]

Do you want any further details or have any questions?

Here are 5 related questions:
1. How do negative exponents affect the value of a number?
2. What is the rule for dividing exponents with the same base?
3. How can you convert powers of larger numbers like \(4\) into powers of \(2\)?
4. How do you multiply and divide fractions in algebraic expressions?
5. What is the reciprocal of a fraction and when is it used?

**Tip:** When working with negative exponents, remember that \( a^{-n} = \frac{1}{a^n} \), which can help simplify complex expressions.

Learn how to simplify the expression (2^(-1) × 4^(-1)) ÷ 2^(-2) using the rules of negative exponents and fractions. This step-by-step solution walks through key concepts such as negative exponents, multiplying and dividing fractions, and simplifying powers of numbers.

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