Let's solve the equation step by step:

Given:

\[
\left(\frac{2}{3}\right)^2 + \left(\frac{6}{5}\right)^2 = \left(\frac{2}{5}\right)^2
\]

### Step 1: Simplify each term
1. \(\left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9}\)
2. \(\left(\frac{6}{5}\right)^2 = \frac{6^2}{5^2} = \frac{36}{25}\)
3. \(\left(\frac{2}{5}\right)^2 = \frac{2^2}{5^2} = \frac{4}{25}\)

So, the equation becomes:

\[
\frac{4}{9} + \frac{36}{25} = \frac{4}{25}
\]

### Step 2: Find a common denominator for the left-hand side

The least common denominator (LCD) of 9 and 25 is 225. So, we need to rewrite the fractions with a denominator of 225.

1. \(\frac{4}{9} = \frac{4 \times 25}{9 \times 25} = \frac{100}{225}\)
2. \(\frac{36}{25} = \frac{36 \times 9}{25 \times 9} = \frac{324}{225}\)

Now, the equation is:

\[
\frac{100}{225} + \frac{324}{225} = \frac{4}{25}
\]

### Step 3: Add the fractions on the left-hand side

\[
\frac{100}{225} + \frac{324}{225} = \frac{424}{225}
\]

So the equation becomes:

\[
\frac{424}{225} = \frac{4}{25}
\]

### Step 4: Compare both sides

Since \(\frac{424}{225} \neq \frac{4}{25}\), the equation is **false**.

Would you like further details or clarifications on any step?

Here are some related questions:
1. What are the properties of exponents when applied to fractions?
2. How do you determine the least common denominator?
3. Can you explain how to simplify fractions after addition?
4. How do you convert improper fractions into mixed numbers?
5. What are the common errors to avoid when solving fractional equations?

**Tip:** When adding fractions, always ensure to find the least common denominator for accuracy.

Step-by-step guide to solving the fractional equation (2/3)^2 + (6/5)^2 = (2/5)^2. This problem covers key concepts such as the addition of fractions, powers of fractions, and how to find the least common denominator. Ideal for students in Grades 6-8.

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