https://file.aiquickdraw.com/mathbot/file/17269407760056ubgrxy8.jpg

The expression in the image is:

\[
\left(\frac{5}{9} + \frac{5}{9}\right) \times \left(2 \frac{2}{3}\right)^2
\]

Let's break it down step by step:

### Step 1: Simplify the Addition
We are asked to add \(\frac{5}{9} + \frac{5}{9}\). Since the denominators are the same, we can simply add the numerators:

\[
\frac{5}{9} + \frac{5}{9} = \frac{10}{9}
\]

### Step 2: Convert the Mixed Number
The second part of the expression involves \(2 \frac{2}{3}\), which is a mixed number. To convert it into an improper fraction:

\[
2 \frac{2}{3} = \frac{3 \times 2 + 2}{3} = \frac{8}{3}
\]

### Step 3: Square the Fraction
Now we need to square \(\frac{8}{3}\):

\[
\left(\frac{8}{3}\right)^2 = \frac{8^2}{3^2} = \frac{64}{9}
\]

### Step 4: Multiply the Two Fractions
Now, we multiply the results of Step 1 and Step 3:

\[
\frac{10}{9} \times \frac{64}{9} = \frac{10 \times 64}{9 \times 9} = \frac{640}{81}
\]

### Step 5: Simplify (if possible)
The fraction \(\frac{640}{81}\) is already in its simplest form.

### Final Answer:
The solution is \(\frac{640}{81}\), which is an improper fraction. As a mixed number:

\[
\frac{640}{81} = 7 \frac{73}{81}
\]

So, the final answer is \(7 \frac{73}{81}\).

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Would you like more details on any of the steps? Here are five related questions to expand on this:

1. How do you convert an improper fraction to a mixed number?
2. What is the general process for adding fractions with different denominators?
3. How do you simplify complex fractions involving powers?
4. Can you explain the properties of mixed numbers and improper fractions?
5. How do you verify that a fraction is in its simplest form?

**Tip**: Always convert mixed numbers to improper fractions before performing operations like multiplication or division.

Use the rules for order of operations to evaluate the following expression: (5/9 + 5/9) * (2 2/3)^2.

Learn how to solve a mathematical expression that involves adding fractions and squaring mixed numbers. This problem explains step-by-step how to apply the order of operations, simplify, and convert mixed numbers into improper fractions.

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