I see that the problem in the image asks to evaluate the expression:

$(4.56^3 + 5.44^3) \div (4.56^2 - 4.56 \times 5.44 + 5.44^2)$

Let me break down and solve this step by step.

Step 1: Calculate $4.56^3 + 5.44^3$

• $4.56^3 = 4.56 \times 4.56 \times 4.56$
• $5.44^3 = 5.44 \times 5.44 \times 5.44$

Step 2: Calculate the denominator $4.56^2 - 4.56 \times 5.44 + 5.44^2$

• $4.56^2 = 4.56 \times 4.56$
• $5.44^2 = 5.44 \times 5.44$
• $4.56 \times 5.44$

Step 3: Divide the result from Step 1 by the result from Step 2.

I will now compute the values.The result of the given expression:

$\frac{4.56^3 + 5.44^3}{4.56^2 - 4.56 \times 5.44 + 5.44^2}$

is approximately $10$.

Would you like further details on this solution or have any other questions?

Here are 5 related questions you might find interesting:

1. How do you simplify expressions involving cubes and squares?
2. What are the properties of cube and square functions?
3. How do you calculate powers of decimals quickly?
4. What is the significance of factoring in similar expressions?
5. Can this expression be solved using a different method, like factoring?

Tip: When handling exponents and complex arithmetic expressions, break them down into smaller, manageable steps for easier computation.