Let's solve the expression \(\frac{64^2 + 16^3}{4^5}\).

1. First, calculate \(64^2\):
   \[
   64^2 = 64 \times 64 = 4096
   \]

2. Next, calculate \(16^3\):
   \[
   16^3 = 16 \times 16 \times 16 = 4096
   \]

3. Add the results:
   \[
   64^2 + 16^3 = 4096 + 4096 = 8192
   \]

4. Now, calculate \(4^5\):
   \[
   4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024
   \]

5. Finally, divide the sum by \(4^5\):
   \[
   \frac{8192}{1024} = 8
   \]

So, the result of the expression \(\frac{64^2 + 16^3}{4^5}\) is **8**.

Would you like more details on any step, or do you have any questions?

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Here are 5 related questions:
1. What is the value of \( \frac{81^2 + 27^3}{3^8} \)?
2. How would you simplify the expression \( \frac{(2^6)^2 + (2^4)^3}{(2^2)^5} \)?
3. What is the value of \( 5^3 + 3^5 \)?
4. How does the expression change if we use a different base, such as \( \frac{10^2 + 5^3}{2^4} \)?
5. How can the laws of exponents be applied to simplify \( \frac{(a^m)^n}{(b^p)^q} \)?

**Tip:** When dealing with large exponents, remember to look for patterns or relationships that can simplify the calculation, such as common bases or factorizations.

Learn how to solve the expression (64^2 + 16^3) / 4^5 with a detailed step-by-step solution. This problem involves arithmetic operations with exponents and division. Suitable for students in Grades 7-9.

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