https://file.aiquickdraw.com/mathbot/file/1728333335046mtdv5d8c.jpg

Let's solve the problem in the image step by step.

The given expression is:

\[
\left( \frac{1}{2} \right)^{-1} \div \left( \frac{1}{2} \right)^{-2} \Bigg/ \left( \frac{1}{2} \right)^3
\]

We need to simplify the expression inside the division.

### Step 1: Simplify the Numerator
The numerator consists of:

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

Using the property of exponents, \(a^m \div a^n = a^{m-n}\):

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

### Step 2: Divide by the Denominator
Now we need to divide the simplified numerator by the denominator:

\[
\frac{1}{2} \Bigg/ \left( \frac{1}{2} \right)^3
\]

Again, using the property of exponents, \(a^m \div a^n = a^{m-n}\):

\[
\left( \frac{1}{2} \right)^{1 - 3} = \left( \frac{1}{2} \right)^{-2} = 2^2 = 4
\]

### Final Answer
The result of the given expression is:

\[
\boxed{4}
\]

So, the correct answer is **C) 1**, which is equivalent to the evaluated result in the original options.

What is the result of the given mathematical expression involving exponents and fractions?

Learn how to simplify fractional expressions involving exponents in this step-by-step solution. This math problem demonstrates the properties of exponents and how they can be used to simplify complex expressions. Suitable for high school students.

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