The text recognition from the image wasn't successful. However, I can visually interpret the mathematical expression from the image.

The given expression is:

$\left( 7^2 - 3^2 \right) + \frac{8}{5} \times \frac{4}{15} - \frac{2}{7} \times \left( 4^2 - 2 \right)$

Let me solve it step by step:

Step 1: Simplify each part inside the parentheses.

• $7^2 = 49$
• $3^2 = 9$
• $7^2 - 3^2 = 49 - 9 = 40$
• $4^2 = 16$
• $4^2 - 2 = 16 - 2 = 14$

Now, the expression looks like: $(40) + \frac{8}{5} \times \frac{4}{15} - \frac{2}{7} \times (14)$

Step 2: Perform the multiplications.

• $\frac{8}{5} \times \frac{4}{15} = \frac{32}{75}$
• $\frac{2}{7} \times 14 = \frac{28}{7} = 4$

Step 3: Combine all terms.

The expression is now: $40 + \frac{32}{75} - 4$

Step 4: Simplify.

$40 - 4 = 36$ Now the expression is: $36 + \frac{32}{75}$

Step 5: Final Addition.

Convert 36 to have the same denominator as $\frac{32}{75}$: $36 = \frac{2700}{75}$ Now add: $\frac{2700}{75} + \frac{32}{75} = \frac{2732}{75}$

Thus, the final result is: $\frac{2732}{75} \approx 36.4267$

The exact value is $\frac{2732}{75}$, or approximately 36.43.

Would you like further clarification or details on any step?

Here are 5 related questions:

1. How do you simplify expressions with exponents inside parentheses?
2. What are the steps to multiply fractions?
3. How do you convert whole numbers to fractions?
4. What are other methods to simplify expressions with fractions?
5. How can you estimate results when working with complex fractions?

Tip: When adding fractions to whole numbers, always convert the whole number into a fraction by using the same denominator!