Let's solve the expression \(\left(\frac{1}{2} + \frac{1}{4}\right)^{-2}\).

### Step 1: Simplify the expression inside the parentheses
First, add \(\frac{1}{2}\) and \(\frac{1}{4}\). To do this, we need a common denominator. The least common denominator of 2 and 4 is 4.

\[
\frac{1}{2} = \frac{2}{4}
\]

Now we can add \(\frac{2}{4}\) and \(\frac{1}{4}\):

\[
\frac{2}{4} + \frac{1}{4} = \frac{3}{4}
\]

### Step 2: Apply the exponent of \(-2\)
Now that we have simplified the expression to \(\frac{3}{4}\), we apply the exponent \(-2\):

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

### Step 3: Square the fraction
\[
\left(\frac{4}{3}\right)^2 = \frac{16}{9}
\]

### Final Answer:
\[
\left(\frac{1}{2} + \frac{1}{4}\right)^{-2} = \frac{16}{9}
\]

Let me know if you need further explanation!

Here are 5 related questions:
1. How do you simplify expressions involving negative exponents?
2. What is the least common denominator, and why is it important for adding fractions?
3. How do you calculate powers of fractions?
4. How would the result change if the exponent were \(-1\) instead of \(-2\)?
5. Can you simplify \(\left(\frac{1}{3} + \frac{1}{6}\right)^{-2}\) similarly?

**Tip:** Remember, a negative exponent means taking the reciprocal of the base and applying the positive exponent.

Learn how to solve ((1/2) + (1/4))^(-2) step by step. This guide covers addition of fractions, applying negative exponents, and calculating powers of fractions. Suitable for students in Grades 6-8.

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