https://r2.erweima.ai/mathbot/image/172672312504533manmff.jpg

The mathematical expression in the image can be interpreted as:

\[
\frac{2^{4 + 2^6}}{20^{2^2} \times 2^1}
\]

Let's break it down and compute its value step by step:

### Steps:
1. **Exponent Calculations**:
   - \( 2^6 = 64 \)
   - \( 4 + 64 = 68 \)
   - \( 2^{68} \)

2. **Denominator Calculations**:
   - \( 2^2 = 4 \)
   - \( 20^4 = 160000 \)
   - \( 2^1 = 2 \)
   - Denominator: \( 160000 \times 2 = 320000 \)

3. **Final Expression**:
   \[
   \frac{2^{68}}{320000}
   \]

Now, I'll calculate the numerical value of this expression.The value of the expression \(\frac{2^{68}}{320000}\) is approximately \( 922,337,203,685,477.6 \).

Would you like a detailed breakdown of any step or further clarification?

Here are 5 related questions for practice:
1. How do you simplify expressions involving exponents?
2. What are the properties of powers of 2, and why are they important in computer science?
3. How would you calculate \( 20^5 \) and \( 2^7 \) manually?
4. How do you handle large numbers in division and multiplication with powers?
5. How does the growth of exponential functions compare to polynomial functions?

**Tip:** When working with very large exponents, knowing logarithmic properties can help simplify the process and check for errors in intermediate steps.

Simplify the expression 2^(4 + 2^6) / (20^(2^2) × 2^1)

Learn how to simplify the exponential expression 2^(4 + 2^6) divided by 20^(2^2) × 2^1. This problem covers exponentiation rules, division of exponential expressions, and the order of operations. Suitable for students in Grades 9-12.

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