https://file.aiquickdraw.com/mathbot/file/1726414363861w4m3m8bv.jpg

Let's analyze and solve the given mathematical expression from the image.

The expression is:

\[
\left( 2^2 \cdot 2^3 - 3^3 \right)^6 : 5^5 + 4 \cdot 3^2 - 5 \cdot 2^3
\]

### Step-by-step solution:

1. **Simplify inside the parentheses**:
   \[
   2^2 \cdot 2^3 = 2^{2+3} = 2^5 = 32
   \]
   \[
   3^3 = 27
   \]
   So,
   \[
   (32 - 27) = 5
   \]

2. **Apply the exponentiation**:
   \[
   (5)^6 = 15625
   \]

3. **Divide by \(5^5\)**:
   \[
   \frac{15625}{5^5} = \frac{15625}{3125} = 5
   \]

4. **Calculate the rest of the terms**:
   \[
   4 \cdot 3^2 = 4 \cdot 9 = 36
   \]
   \[
   5 \cdot 2^3 = 5 \cdot 8 = 40
   \]

5. **Final expression**:
   \[
   5 + 36 - 40 = 1
   \]

### Final Answer:
The value of the given expression is \(1\).

Would you like more details or have any questions?

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Here are 5 related questions to deepen understanding:
1. How do we simplify products of powers with the same base?
2. What is the rule for dividing exponents with the same base?
3. How do exponent laws apply when simplifying more complex expressions?
4. What are some shortcuts for calculating higher powers of small numbers?
5. How do we handle expressions with multiple operations (exponents, multiplication, and division)?

**Tip**: Always simplify expressions inside parentheses first before applying powers and other operations.

(2^2 · 2^3 - 3^3)^6 ÷ 5^5 + 4 · 3^2 - 5 · 2^3

Learn how to simplify the exponential expression (2^2 · 2^3 - 3^3)^6 ÷ 5^5 + 4 · 3^2 - 5 · 2^3. Follow the detailed step-by-step solution involving exponent laws and order of operations. Suitable for students in Grades 9-10.

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