Find the value of
`(2^(-1) xx 4^(-1) ) div 2^(-2)`

Answer

To solve the expression \( (2^{-1} \times 4^{-1}) \div 2^{-2} \), we will follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ (2^{-1} \times 4^{-1}) \div 2^{-2} \]

### Step 2: Convert \(4^{-1}\) to base 2
Since \(4\) can be expressed as \(2^2\), we can rewrite \(4^{-1}\) as:
\[ 4^{-1} = (2^2)^{-1} = 2^{-2} \]
Now, substitute this back into the expression:
\[ (2^{-1} \times 2^{-2}) \div 2^{-2} \]

### Step 3: Combine the powers of 2 in the numerator
Using the property of exponents \(a^m \times a^n = a^{m+n}\), we can combine the powers in the numerator:
\[ 2^{-1} \times 2^{-2} = 2^{-1 + (-2)} = 2^{-3} \]
So now our expression looks like:
\[ 2^{-3} \div 2^{-2} \]

### Step 4: Apply the division of powers
Using the property of exponents \(a^m \div a^n = a^{m-n}\), we can simplify the expression:
\[ 2^{-3} \div 2^{-2} = 2^{-3 - (-2)} = 2^{-3 + 2} = 2^{-1} \]

### Step 5: Convert back to a fraction
Finally, we know that \(2^{-1}\) can be expressed as:
\[ 2^{-1} = \frac{1}{2} \]

### Final Answer
Thus, the value of the expression \( (2^{-1} \times 4^{-1}) \div 2^{-2} \) is:
\[ \frac{1}{2} \]

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