To solve the expression \(5^5 \cdot 2^5 \cdot 10\), let's break it down step by step.

### Step 1: Simplify \(5^5 \cdot 2^5\)
We can recognize that \(5^5 \cdot 2^5\) can be rewritten using the property of exponents:
\[
5^5 \cdot 2^5 = (5 \cdot 2)^5 = 10^5
\]
So, \(5^5 \cdot 2^5 = 10^5\).

### Step 2: Multiply by 10
Now, we multiply \(10^5\) by 10:
\[
10^5 \cdot 10 = 10^{5+1} = 10^6
\]
Thus, the expression simplifies to \(10^6\).

### Final Answer:
\[
5^5 \cdot 2^5 \cdot 10 = 10^6 = 1,000,000
\]

Would you like further details or have any questions?

### Related Questions:
1. How would you simplify \(3^4 \cdot 4^4 \cdot 5\)?
2. What is the value of \(6^5 \cdot 5^5 \cdot 2\)?
3. How does the property of exponents apply to \(2^3 \cdot 4^3\)?
4. Can you express \(7^3 \cdot 3^3 \cdot 21\) in a similar way?
5. What is the result of \(10^6 \cdot 10^2\)?

### Tip:
When multiplying powers with the same base, you can simply add the exponents!

Discover how to simplify the expression 5^5 ⋅ 2^5 ⋅ 10 step-by-step with detailed explanations and calculations. This problem involves exponents and multiplication of powers, culminating in the value of 10^6. Suitable for Grades 7-9.

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